
Stephan El Shaarawy and Bryan Cristante scored in the first half to give Roma a grip on the game after their loss to AC Milan before the international break.
But Chievo, who were beaten 6-1 by Fiorentina in their last game and deducted three points by the Italian Football Federation for false accounting, battled back in the second half.
Valter Birsa pulled a goal back after 52 minutes before Polish striker Mariusz Stępiński grabbed a point for the club from Verona by scoring a goal seven minutes from time.
Roma goalkeeper Robin Olsen did well to clear a final Emanuele Giaccherini effort to save a point for the Romans.
Roma are now seventh with five points from four games, four points behind champions Juventus who host Sassuolo later on Sunday with Cristiano Ronaldo still waiting for his first goal.
Chievo are propping up the table on -1 points after their deduction during the week.