The gunman apparently shot the hostage and then himself, police said.
"At no time did the Chicago Police Department fire a weapon," 1st Deputy Superintendent Dana Starks said at a press briefing.
Starks said the gunman and victim were the only people found in the apartment. An additional hostage may have escaped earlier, he said.
The standoff began early Thursday after an armed man took his young neighbor hostage inside their apartment building.
Police SWAT team members entered the apartment just after 1 a.m. Friday after officers heard a shot fired, Starks said.
Inside, police found the gunman and his 22-year-old hostage gravely wounded. The two were transported to a hospital and later pronounced dead, Starks said.
Police have not yet released their identities. Starks confirmed that the two were neighbors, but added "the extent of their relationship we don't know."
Sherry McKenzie said Thursday that one of the hostages was her niece, Tasha Cooks, 22.
Click to watch neighbors' accounts of the gunman
She said Cooks used the apartment phone to call her great-grandmother earlier in the day. When asked if she was OK, Cooks responded, "Not really," and hung up, according to McKenzie.
The gunman's sister pleaded with her brother to cooperate with authorities Thursday afternoon. Later, frustrated relatives and neighbors began shouting at police to do more to end the standoff.
Officers had been negotiating with the man, and Superintendent Phil Cline had held out hope late Thursday that the situation could be ended peacefully.