In fifth place is D.C. United with 36 points. And the Union's next game is Sunday at United.
The Union believe it's too early to think about next year. Next week is all that's on their minds.
"We're not throwing in the towel," interim coach John Hackworth said.
The Union were without captain Carlos Valdes and midfielder Gabriel Gomez, who had national-team duties. Valdes was training with the Colombian team in preparation for World Cup qualifying matches in September. Gomez will play for Panama in Wednesday's friendly in Portugal.
Forward Jack McInerney sat out because of a red card he received in the previous game.
Former Fire defender Bakary Soumare, who had been sidelined by a knee injury, made his first start for the Union in Valdes' central-defender spot.
"I was a little rusty, obviously, but I'm glad I got to play a little bit and I was feeling good and my knee had no pain, so I was happy about that," Soumare said.
In the 11th minute, Union midfielder Gabe Farfan, positioned at the far post, headed a Freddy Adu cross wide for the game's best early chance.
But the Union struck in the 34th minute on a cross-turned-own-goal.
Adu sent a cross on goal, and teammate Chandler Hoffman said he flicked it with his head, although it was difficult to tell, even on replay.
Either way, the ball zoomed past Chicago keeper Sean Johnson. Fire defender Jalil Anibaba, trailing the play, knocked it into the net.
The Fire responded with two goals late in the half.
Chicago's Chris Rolfe scored the equalizer. Teammate Sherjill MacDonald beat Soumare down the right end line and crossed it to Rolfe, who one-timed it just outside the 6-yard line in the 43d minute.
Arne Friedrich headed in a Marco Pappa corner kick during first-half stoppage time.
"We were up, 1-0, and to give two late in the first half wasn't good timing," Hoffman said.
In the second half, the Union came out aggressive. Midfielder Brian Carroll headed a corner kick by Michael Farfan just over the goal in the 50th minute.
Chicago went up, 3-1, in the 56th minute when Rolfe, who entered the game with two goals, blasted a shot from just outside the box past keeper Zac MacMath, who tipped the ball.
After that, the Union had to open things up and gamble, which created opportunities for both teams.
MacMath kept the Union in the game when he made a kick-save of a breakaway by MacDonald in the 60th minute. In the 62d minute, Michael Farfan hit the post from just outside the box.
It was that kind of night.
"I don't think anybody thinks we are out of the playoff picture," MacMath said. "All of us are looking forward to next weekend and getting three points back."
Contact Marc Narducci at 856-779-3225 or firstname.lastname@example.org. Follow on Twitter @sjnard.