A career-best unbeaten 73 by all-rounder Liam Patterson-White led a Notts recovery from 119-6 to 273 all out at Trent Bridge.
Warwickshire were then reduced to 24-2 at the close, with England batsman Dom Sibley unable to bat due to a finger injury.
Patterson-White, a 22-year-old left-arm spinner playing only his seventh first-class match, batted for three hours and eight minutes and hit 12 boundaries, striking the ball cleanly on both sides of the wicket.
Skipper Will Rhodes, fourth seamer in the absence of the injured Liam Norwell, was the most successful Warwickshire bowler with4-53.
With England’s Dom Sibley not taking his usual place at the top of the order, Warwickshire hoped to survive the 10 overs they faced at the end of the day but instead lost Rob Yates and debutant Indian Test batsman Hanuma Vihari without scoring, the latter a victim for England paceman Stuart Broad on his return to county action.
Despite losing two wickets, Bears skipper Rhodes was pleased with his side’s efforts.
“I think it has been a pretty good day for us,” he said. “When the opposition chose to bat first and you keep them to under 300 you feel you’ve done well, especially at Trent Bridge which is a really fast scoring ground.”
“It would have been nice to get those last couple of Notts wickets a bit sooner but Patterson-White and Chappell played pretty well after we threw a lot at them, to be fair.
A Matt Critchley century and 98 from Leus du Plooy put hosts Derbyshire in a strong position against Worcestershire.
Critchley followed his two half-centuries at Edgbaston last week with 109 as Derbyshire closed day one on 360-8 which also included an unbeaten 65 from Harvey Hosein and 50 by Billy Godleman.
Worcestershire spilled five catches but they fought back after tea with Ed Barnard and Alzarri Joseph both taking two wickets in two balls.
Worcestershire bowling coach Alan Richardson said: “It was a tough day at the office, if we are brutally honest with ourselves we weren’t quite at the races for long enough periods with the ball.
“Our catching let us down a bit as well but the boys stuck at it and we got our rewards in that last half-an-hour. But we put ourselves under a bit of pressure by not quite executing our plans.”