The stalemate means Milan are without a win in six games in all competitions, and it also brought to an end their run of 14 consecutive victories over their hosts.
Chievo themselves are without a win in eight matches, and they could have made it even worse for Allegri and Milan had Luca Rigoni not missed a gilt-edged opportunity at the start of the second half.
Milan created little, going closest to scoring when second-half substitute Robinho struck the post late on before skipper Riccardo Montolivo was sent off seven minutes from time after picking up a second caution.
Both sides finished with 10 men as Chievo club captain Sergio Pellissier was also dismissed in stoppage time after coming on as a substitute.
The hosts were unchanged from last week's draw at Bologna, while Allegri made just one alteration from the side that lost in Barcelona in midweek as Alessandro Matri returned to the front line in place of Robinho.
After a quiet opening, Chievo were first to threaten in the 17th minute as Marcelo Estigarribia stung the palms of Christian Abbiati from 25 yards before Bostjan Cesar fired wide when well placed following the resulting corner.
Milan's response was immediate, though, as home keeper Christian Puggioni had to move low to his left to smother Sulley Muntari's effort from distance after a surging run from the Ghanaian.
With chances at a premium in a scrappy first half, Andrea Poli wasted a good opportunity to break the deadlock for Milan three minutes before the break when he dragged his shot wide after being found by Matri inside the area.
Six minutes after the restart, the hosts spurned a golden opportunity to open the scoring.
Cyril Thereau's shot was parried by Abbiati and the rebound ran perfectly for Rigoni, who, from a slight angle, hit the side netting when presented with an open goal six yards out.
Puggioni was called into serious action for the first time on the hour mark, the goalkeeper beating away Urby Emanuelson's swerving long-range effort before diving full length to his left to keep out Philippe Mexes' volley from 20 yards.
The hosts had a goal disallowed for offside with 16 minutes remaining when Thereau poked the ball beyond Abbiati but the linesman had raised his flag, with replays suggesting he may have just been level with the last defender.
Once again Milan's response was swift, Poli firing wide from the edge of the area, before Robinho missed Milan's best chance of the game, striking the base of the post from 12 yards after being played in by Muntari.
Three minutes later Montolivo was dismissed for a second bookable offence after a challenge from behind on Perparim Hetemaj.
Despite their temporary numerical advantage, Matri fired another good chance wide a minute later before Pellissier saw red as Milan - and Allegri's - troubled season continued.
