Phil Brown's men took the lead on 30 minutes thanks to a thumping header from defender Stephen Mouyokolo, only for Didier Drogba to grab the equaliser with a pin-point free-kick just before half time.
The visitors came closest in the second half through Drogba and Daniel Sturridge, but Hull fought hard to ensure the points were shared.
Frank Lampard came close for Chelsea early on with a rasping shot from 30 yards, stinging the hands of keeper Boaz Myhill. The rebound fell to the in-form Nicolas Anelka, but he failed to control the ball; sending it spinning out for a goal-kick.
Carlo Ancelotti's men then had a great chance to take the lead as a cross from Branislav Ivanovic found the head of an unmarked Michael Ballack, but the Germany international directed his diving effort straight at Myhill, who was able to make a comfortable save.
Moments later Hull broke the deadlock when a curling corner from Hunt was met by a towering Mouyokolo, whose powering header from close range left keeper Petr Cech with no chance.
However, the visitors were back level just minutes before half-time as George Boateng scythed down Anelka on the edge of the box allowing Drogba to step up and fire a free-kick into bottom corner of the net to register his eighth goal in nine games for the Blues.
Moyokuolo could have scored a second for Hull in first-half injury time as Tom Cairney floated in a dangerous ball towards the French defender, however, Anthony Gardner powered his way in front of his colleague and sent the ball looping over the bar.
Chelsea came close to taking the lead early in the second half as a corner from Florent Malouda was met with a thumping header from Drogba, but keeper Myhill managed to make a tremendous save down to his right.
John Terry powered in a header in the following melee, but again Myhill was equal to it; palming the ball to safety.
Drogba had another chance on the 75-minute mark, but his header from an Ivanovic cross looped just over the bar.
Substitute Sturridge nearly stole all three points for the visitors in injury time, but his long-range half-volley was well brilliantly turned away by Myhill.