Chelsea have failed to find a breakthrough against a resilient Hull City side, who may consider themselves unlucky not to be ahead.
The Blues, who haven't beaten a promoted team away from home in their last six attempts, probed in the opening minutes and enjoyed much of the early possession.
However, Hull had the first chance of any note when Ahmed Elmohamady drilled a shot from 25 yards that was gathered by Petr Cech.
The visitors came close to falling behind midway through the first period when another low effort from the edge of the area, this time from Jake Livermore, forced another save from the Chelsea keeper.
Hull continued to frustrate Jose Mourinho's charges and when John Terry uncharacteristically gave the ball away inside his own box, Yannick Sagbo unleashed a fierce shot that went narrowly wide of Cech's post.
Chelsea's first clear-cut opportunity came just after the half-hour mark when Eden Hazard's square ball found Oscar, but the Brazilian was thwarted by Allan McGregor's reactions.
With half time approaching, David Luiz's fizzing free kick brought another fine save out of the Hull shot-stopper.
The West London club won the return fixture 2-0 on the opening day of the season.
