Chelsea will play the final 22 minutes at Villa Park with 10 men after Willian was dismissed for a second yellow card.
The Brazilian, booked in the first half, saw red after referee Chris Foy adjudged he had fouled Fabian Delph.
Jose Mourinho’s side have dominated large chunks of the second half but have yet to break down a well-drilled Aston Villa defence.
The Blues have been encamped in Villa territory but their final ball has often been found wanting, with Eden Hazard allowing Karim El Ahmadi a clearance inside the six-yard box when he chose to pass instead of shoot.
Hazard later found Oscar with a short corner but the Brazilian’s tame shot was comfortable for Villa keeper Brad Guzan to gather.
At the other end, Christian Benteke swept a shot just wide of the post after being found by Andreas Weimann.
Chelsea thought they had taken the lead five minutes before half-time but Nemanja Matic’s close-range finish was ruled out for handball.
Benteke had Villa’s best chance in the first half with well-struck volley just wide of Petr Cech’s far post.
After Manchester City’s 2-0 win at Hull earlier in the day, Chelsea will not be wanting to drop crucial points in the title race.
Chelsea (4-2-3-1): Cech; Ivanovic, Cahill, Terry, Azpilicueta; Matic, Ramires; Willian, Oscar, Hazard; Torres. Subs: Schwarzer, Kalas, Mikel, Lampard, Schurrle, Salah, Ba.