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.