Prosecutors say Adame set the fire after a dispute with a woman who lived in the building at 4246 W. 63rd Street in Chicago. She was not there at the time.
The man who lived in an adjacent unit, James Maca, 60, was killed.
Officials say Adame used gasoline to start the fire in the second floor apartment.
Adame was taken into custody on Thursday. He faces a federal arson charge.