Wayne Rooney featured despite the Blues' public interest in his services yet neither team could make a decisive breakthrough in a match of few chances on Monday night
The fixture marked the first time that David Moyes locked horns with Jose Mourinho as United manager but neither manager could gain the psychological upper hand, although the point puts the Blues clear at the top of the Premier League.
Oscar tried to prise open a tight United defense in a lackluster first half but twice wasted good opportunities with weak efforts straight at David de Gea. Robin van Persie had United's best effort when he hit the side netting from inside the area.
The second half followed a similar pattern and England international Danny Welbeck will rue his wastefulness after digging an effort wide after good work from Wayne Rooney. United also had claims for a penalty when a Tom Cleverley shot struck Frank Lampard's hand in the box.
Moyes named Rooney in his starting XI for the first time, with the striker the subject of two rejected bids during the close-season from Monday night's opposition. Ryan Giggs dropped to the bench to allow for his inclusion.
Chelsea started the game with a surprise as Andre Schurrle led the line. Kevin De Bruyne was also given the nod as Juan Mata and Demba Ba were omitted from the side that started against Aston Villa on Wednesday.
Both sides struggled to create openings in a tepid opening 45 minutes. It was the away side which had the first chance in the 10th minute when a low De Bruyne cross rebounded to Oscar who hit a tame effort straight at De Gea.
Chelsea had managed to quash the threat Van Persie for the opening 20 minutes but the Dutchman had United's first meaningful effort. Michael Carrick dispossessed Ramires in midfield and the former Arsenal man picked up the loose ball on the edge of the box but he went too wide before firing his effort against the side netting.
Rooney then had his first effort on goal. He showed a neat piece of skill to feint inside Gary Cahill but his shot from 20 yards was weak and rolled harmlessly to Petr Cech.
United was beginning to enjoy more of the ball and, in the 38th minute, Phil Jones's low cross was only half-cleared by John Terry and Cleverley hit a first-time shot from 20 yards that cleared the crossbar.
The half ended with a weak shot from Oscar after a series of neat passes in the Chelsea midfield - the Brazilian will feel that he could have done more to trouble De Gea.
After a slow start to the second half, United should have taken the lead after 56 minutes. Rooney showed good control just outside the area before slipping a neat through-ball to Welbeck but the striker fluffed his lines as he chipped his effort over from 10 yards.
Cahill was unlucky with a 30-yard drive that De Gea got down well to save, before United had claims for a penalty.
Cleverley's half-volley hit Lampard's hand in the area but referee Martin Atkinson deemed that the midfielder had not deliberately made contact with the shot.
Rooney almost had the last say late on when he tested Cech with a strong 25-yard effort. The shot may have been going wide but the Chelsea man took no chances.
With two minutes remaining, United had another penalty shout when John Obi Mikel turned into Van Persie's volley but the decision would have been harsh on the Nigerian who knew had no time to dodge the shot.