Training partner Florence Kiplagat defended her women's title, winning by almost two minutes.
Kirui, a former two-time world champion, took the men's race in two hours, 11 minutes and 23 seconds and celebrated afterward with Kiplagat, who finished in 2:21:32.
"It was a matter of life and death," Kirui said of holding on to defeat Chumba. "It was amazing."
After a slow pace for long stretches at the start, Kirui and Chumba settled in for a tactical duel over the final miles.
Both took turns leading before Kirui pushed ahead with less than a mile to go.
Chumba, who had only arrived in Chicago on Friday after visa problems, tried to come back in the closing stages but could not make up the difference.
He finished three seconds back with Kenyan Gideon Kipketer third. Kiplagat broke away after 19 miles in the women's race and was never challenged by a quality field.
Neither Kirui nor Kiplagat were selected for Kenya's Olympic team and Kiplagat said she used her omission as motivation."I was not selected for the Olympics, so I wanted to win Chicago two years in a row," Kiplagat said.
"I was very confident." Compatriot Edna Kiplagat took second in 2:23:28 and another Kenyan, Valentine Kipketer, was third.
American Tatyana McFadden claimed her sixth consecutive Chicago women's wheelchair title with a narrow win over Swiss Manuela Schaer.
McFadden, the Olympic silver medallist, took the victory in 1:42.29, the same time as Schaer. Swiss Marcel Hug edged defending champion Kurt Fearnley of Australia for the men's wheelchair championship.
Hug clocked 1:32:57 with Fearnley a second back.
(Reporting by Gene Cherry; editing by Neil Robinson)
