The seventh-placed Turin side lie five points behind Udinese, who are in the fourth and final Champions League qualifying spot with two games left, and Juve are not even assured of playing Europa League football next term in their as yet unnamed new stadium.
The point means mid-table Chievo are now safe from relegation.
Once mighty Juve were cruising after Alessandro Del Piero celebrated his new one-year contract with a 13th minute penalty before strike partner Alessandro Matri exposed poor defending to make it 2-0 early in the second half.
But such is the twice European champions's brittle confidence after two seasons of woe that few fans in the nervous Stadio Olimpico were surprised when the visitors retaliated.
Chievo pulled one back on 68 minutes when Fernando Uribe bundled the ball home and they equalised almost immediately when Gennaro Sardo calmly finished from the edge of the area after Sergio Pellissier had struck the post.
The Verona-based side, nicknamed the Flying Donkeys, could easily have won in the closing stages after Juve goalkeeper Gianluigi Buffon charged rashly out of goal but the hosts also hit the post through Luca Toni late on in an entertaining game.
Juventus boss Luigi Del Neri, who famously coached Chievo to great success in the previous decade, is fighting to keep his job amid media speculation linking Italy's most successful domestic club with a host of managers including Napoli's Walter Mazzarri.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
