And the Browns have a 23-14 lead over the Steelers with 9:29 remaining.
Chubb scored on a 1-yard run on fourth down to give the Browns a two-score lead. Cade York, who missed a PAT in the first half, made the extra point. York kicked a 34-yard field goal in the third quarter.
The Steelers led 14-13 at halftime, but they have only 16 plays and 50 yards in the second half. They have punted on all three second-half possessions.
Chubb has 105 yards on 15 carries and Kareem Hunt has 11 carries for 45 yards.
The Steelers have lost cornerback Ahkello Witherspoon with a hamstring injury. He will not return.