Accam scored twice in the opening eight minutes, the first coming in the third minute off a cross from Matt Polster. In the eighth, he got behind the defense after a long pass from Bastian Schweinsteiger and easily scored.
In the 52nd, Accam picked up an assist with a short pass between two defenders to league scoring leader Nemanja Nikolic, who put the ball in from the right side for his 14th goal.
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Playing his third MLS season, Accam completed the hat trick with his 10th goal of the season on a penalty kick in the 63rd after he was taken down in the box by Scott Sutter.
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Chicago (10-3-4) extended its unbeaten streak to nine and is undefeated in 12 home matches, including a team-record seven in a row this year. Orlando (7-6-5), which did not have a shot on target, is 1-5-2 on the road.
The Fire's only previous competitive win against Orlando came in the 2015 U.S. Open Cup.