Skipper Chawla scored his fifth first-class century, during which he faced 279 deliveries and hit 14 fours and six sixes, as Uttar Pradesh stretched the score from overnight 411 for seven to 500 for nine declared at Bhamashah Stadium.
Tamil Nadu scored 128 for two in their second innings with opener Abhinav Mukund hitting an unbeaten 149-ball 56 while Test specialist Murali Vijay contributing 38 off 52 balls before being trapped lbw by Chawla.
Earlier, Chawla continued from where he had left yesterday as he launched Aushik Srinivas for three huge sixes in an over, the third of which took him past his 150.
However, Chawla was soon dismissed by Srinivas for his career-best 153. He added a record 177 runs for the eighth wicket with Amit Mishra, the other overnight batsman, who also scored a gritty 143-ball 59.
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Brief Scores:
Tamil Nadu 1st innings: 297 & 128 for 2 in 48 overs (Abhinav Mukund 56 not out; Piyush Chawla 2/17)