But less reported is his record of supporting immigrant communities as archbishop of Denver and strong advocacy on behalf of social services over the years, which, at times, has seemed downright progressive.
Chaput, a diminutive and boyish 66-year-old, does not necessarily see those stances at the ends of the political spectrum as contradictory.
"I don't know that I'd describe myself as outspoken. I'm public about things," he said. "The role of the church is to be a voice on principles."
On Sept. 8, Chaput will be installed at the helm of the Archdiocese of Philadelphia, in the heart of one of the most socially liberal regions in the country.
This raises the question of whether his new flock, used to the often opaque, quiet leadership of Cardinal Justin Rigali, is ready for a vocal, politically engaged proponent of hard-line Catholic orthodoxy.
"He's not afraid to ask questions or support positions that make even very good, practicing Catholics uncomfortable," said Francis X. Maier, Chaput's longtime chancellor and the man the archbishop describes as his left brain. "The archbishop believes that leaders should be leaders, and he has no problem being that leader."
Two days after Tuesday's announcement of his new post, Chaput gathered parishioners, clergy, and reporters in a sparsely decorated conference room in the basement of the John Paul II Center for the New Evangelization, a Spanish-mission-style compound on the west side of Denver that serves as headquarters for the archdiocese.
From the moment he entered the room, the love he has engendered among many of Colorado's Catholics was evident. Old and young flocked to his side, eager to greet him. Somehow, he managed to respond to each in brief encounters punctuated with firm, lingering handshakes and frequent jokes. It was as if he were having dozens of a private conversations at once.
That openness - displayed over and over during his farewell news conference Wednesday - is frequently noted when people in Denver are asked to describe their departing archbishop.
"He has an intensity that is almost palpable," said David Trickett, president of Denver's Iliff School of Theology. "He is focused, he is disciplined, and he attends to detail. One feels that in his presence, you are being attended to personally."
Chaput spends nearly three hours a day responding to every letter and e-mail he receives, a practice he fears he will be unable to continue in Philadelphia, an archdiocese of 1.5 million compared with Denver's 550,000.
A movie buff and fan of science fiction, he once delivered a homily on why The Exorcist was one of his favorite films. He can discourse as fluently on Star Trek and Wyoming's best fishing spots as he can on the finer points of canon law - qualities that make him popular among younger parishioners.
When a nervous Jim Crisman interviewed with the archbishop to enroll in Denver's seminary, Chaput immediately put him at ease.
"We played racquetball and then went to Applebee's," said Crisman, now director of priestly vocations for the archdiocese.
Maintaining strong ties to pop culture and the day-to-day world of his flock has been important to Chaput in Denver. For while he has urged Catholics to take their church's teachings into all aspects of secular life, it is just as important to him that the church provide its members with a way to view their secular life through a Catholic lens, Maier said.
"The culture forms people," he said. "If you don't know the culture, you don't know how to reach the people."
That lesson was hammered home from Chaput's earliest days in the priesthood.
The son of a French Canadian father and an American mother of the Potawatomi tribe, Chaput was one of three siblings raised in rural Concordia, Kan. Although he briefly considered a career as a movie stuntman in his youth, he said, by 13 he felt called to the clergy.
"It was part of my life from the very beginning," the archbishop said. "And my family encouraged it."
When Chaput joined the Order of Friars Minor Capuchin in 1965, he entered a Catholic Church in a period of deep soul searching.
Three years before, Pope John XXIII had convened the Second Vatican Council to address concerns that the hierarchy had become increasingly divorced from modern political and social realities.
Reform-minded clergy pushed for more leadership roles for laity, greater use of vernacular languages in the traditionally Latin Masses, and a more local form of governance helmed by bishops.
While progressive theologians regard Vatican II as a great leap forward in the church's relation to modern mores, Chaput emerged from the '60s interpreting its significance differently:
The church could not afford to sink into irrelevance by ignoring the outside world. But rather than water down ecclesiastical teaching to accommodate shifting social attitudes, the clergy must aggressively engage the secular, demonstrating that orthodox Catholic teaching applies to life outside the pews.
"Asking Catholics to keep their faith out of public affairs amounts to telling them to be barren, to behave as if they were neutered," he wrote in his 2008 book, Render Unto Caesar: Serving the Nation by Living Our Catholic Beliefs in Political Life.
This conclusion has guided him throughout his career - first as a parish priest in the early 1980s at a suburban Denver church; then as bishop of Rapid City, S.D., a post he earned in 1988; and finally his appointment as archbishop of Denver in 1997.
This unwavering commitment to secular engagement also lies at the core of nearly every clash he has had with critics, and after 14 years in Denver he has had a few.
"I can't tell you the number of people I know who don't go to Mass anymore," said Gwyn Green, a lifelong Catholic and former Colorado state representative. She blames Chaput's politics.
Her clashes with Chaput in the mid-2000s over a bill that would have extended the civil statute of limitations on clergy sex-abuse cases prompted her decision to leave the church. "I was made to feel unwelcome by the administration of my parish."
Chaput's frequent forays into the political realm have drawn national media attention - much of it negative.
Most famously, The New York Times quoted him during the 2004 presidential election as suggesting that anyone who intended to vote for Kerry, a Catholic who supports abortion rights, was "cooperating with evil" and needed to "go to confession." Chaput maintains his comments were taken out of context.
Soon after President Obama's inauguration, Chaput decried what he called a "spirit of adulation bordering on servility" toward the president by some Catholics despite Obama's record on abortion.
And last year, when a lesbian couple in Boulder tried to reenroll their children in a parochial school, he refused them on the ground that their lifestyle contradicted Catholic teachings.
His ventures into politics have at times angered more Republican-minded Catholics as well. In the face of rising tensions between a growing Hispanic population in suburban Denver and the Anglo parishioners who traditionally made up the area's church community during the early 2000s, Chaput insisted that the immigrant population deserved respect and brought in a professional mediator to help them work out their differences.
"I feel like my church has been stolen from me," one Anglo man told the Denver Post in 2003, reacting to Chaput's handling of the situation.
But even those who have clashed most frequently with Chaput credit him with consistency in his views. The archbishop agreed, explaining his most controversial public stances not as attempts to topple the church-state barrier but as natural extensions of Catholic teaching.
His statements against Kerry, then, were less a tacit endorsement of George W. Bush than a call for parishioners to vote the antiabortion tenets of their religion. (In fact, his advisers said that while Chaput had enjoyed a collegial relationship with Bush, the president's "evangelical optimism unconnected with reality" had made the archbishop nervous.)
"His strength as a leader is that he leads by ideas," said John Kane, a professor of religion at the Jesuit Regis University who ran Denver's reform-minded Catholic newsletter, Leaven, for more than a decade. "You can stand strong for your ideas and make them the basis of your decisions, but when you're meeting people in concrete situations it's important to have some sort of personal flexibility."
Chaput's flexibility will surely be tested in Philadelphia, where he will manage an archdiocese in the midst of a severe crisis of confidence.
A March grand jury report blamed top leaders for covering up years of clergy sex abuse. Two priests, a Catholic school teacher, and a monsignor stand indicted on charges of either sexually abusing children or endangering them. And 21 accused priests remain suspended as part of the most sweeping action in the Catholic sex-abuse scandal in the United States.
Chaput's handling of abuse cases in Denver has received mixed reviews. His archdiocese was one of the first to implement a zero-tolerance policy for priests accused of inappropriate contact with young parishioners.
When accusations have surfaced, he has acted swiftly, removing pastors from clerical duties immediately and reporting the accusations to police. Even some accusers speak highly of Chaput's handling of their allegations.
"He sat there and took it," said Tom Koldeway, who sued a Denver priest in 2005 and remembers Chaput's sitting in on his mediation sessions with the archdiocese. "He was very receptive to what we had to say."
But Chaput has also fought ferociously against government proposals to open up the civil statutes of limitations on sex-abuse cases, which would allow alleged victims of abuse to file complaints in court decades later.
He has defended his stance by saying such bills apply a different standard to the church.
With the Pennsylvania General Assembly facing a similar bill, Chaput is likely to find himself fighting the same fight here.
But it is, after all, in that venue where Chaput has always shined.
"Whenever the church is criticized, she understands herself better and is purified," he wrote in a 2004 column in the Denver Catholic Register. "That's sad and difficult, and a judgment on a generation of Catholic leadership. But it may be exactly the moment of truth the church needs."
To watch a video about Philadelphia's new archbishop, go to www.philly.com/chaput
Contact staff writer Jeremy Roebuck at 267-564-5218, firstname.lastname@example.org, or @inqmontco on Twitter. Read his blog, "MontCo Memo," at www.philly.com/montcomemo