Balfour, who faces a mandatory life prison sentence, showed no emotion.
Jurors deliberated for three days before reaching their verdict against Balfour, 31, a former gang member who was the estranged husband of Hudson's sister at the time of the triple murders.
With no surviving witnesses to the Oct. 24, 2008, slayings or fingerprints, prosecutors built a circumstantial case against Balfour by calling 83 witnesses over 11 days of testimony. Witnesses said he threatened to kill the entire family if Julia Hudson spurned him.
Balfour's attorneys proposed an alternate theory: that someone else in the crime-ridden neighborhood on Chicago's South Side targeted the family because of alleged crack-cocaine dealing by Hudson's brother, Jason. During the 30 minutes in which they called just two witnesses, however, they presented no evidence to support that theory.
Public defender Amy Thompson said she would appeal the verdict. "It has always been our position and it still is that William Balfour is innocent of these murders," she said.
Cook County State's Attorney Anita Alvarez reiterated what prosecutors had told jurors, saying the evidence against Balfour was overwhelming.
The verdict came shortly after jurors sent the judge a note saying they were split. The jury did not say it was giving up, though.
"We are trying," jurors said in their note.