At stumps on the second day, Alam was batting on 93 while Buvnesh Kumar was giving him company on 34, at the Vidarbha Cricket Association Ground.
Chawla got out after striking 85 off 113 balls and the legspinner hit eights fours and three sixes during his stay in the middle.
Alam faced 195 balls during his patient knock and struck eight boundaries.
Resuming on 248 for four with Parvinder Singh and Amir Khan at the crease, Uttar Pradesh, after losing a few wickets, rode on a 139-run partnership for the seventh wicket between Alam and Chawla to consolidate their position.
Chawla was unfortunate to have missed a century as he was dismissed by Gaurav Upadhyaya when 15 runs short of the landmark.
Sandeep Singh was the best bowler for Vidarbha as he finished the day with three wickets. Upadhaya bagged two for 96.
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Brief scores:
Uttar Pradesh 1st innings: 524/7 in 180 overs (Mukul Dagar 116, Arish Alam batting 93, Mohammad Kaif 85, Piyush Chawla 85; Sandeep Singh 3/75).