Although United had the better of David Moyes' first home Premier League game in charge, they lacked the authority to exert the kind of sustained pressure which might have shaken John Terry out of his defensive superiority.
Last season's Golden Boot winner Robin van Persie barely had a chance of note, his best opportunity coming three minutes from time when his goalbound volley deflected to safety off Gary Cahill and John Obi Mikel.
Jose Mourinho has made no secret of his desire to sign Wayne Rooney at some point in the next seven days.
Playing in a deeper role than Mourinho would use him for Chelsea, the England forward did well on his first start since April, and tested Petr Cech with one late strike.
If anyone looked likely to break the deadlock it was Rooney, who was cheered by both sets of supporters.
It did not happen though as both sides were forced to settle for a point which, under the circumstances, neither will be too unhappy with.
When United last played a Premier League game at Old Trafford, Sir Alex Ferguson told the club's supporters they had a duty to get behind his replacement.
They heeded that clarion call, chanting Moyes' name at regular intervals and baiting Mourinho for "wanting his job".
It was part of an amusing exchange of crowd banter, that included Wayne Rooney being cheered by both sets of supporters, Chelsea's adding a cheeky: "We'll see you next week" after a run at Gary Cahill.
Chelsea have already had two bids for the 27-year-old turned down, with a third expected later this week.
The reason why was obvious from Mourinho's team selection.
Evidently he does not believe Fernando Torres is good enough, preferring instead the 'false nine' concept he came up against when he faced Barcelona during his time at Real Madrid.
Amazingly, this did not include Juan Mata, who most United fans would happily exchange for Rooney, who made his first start since April.
As it turned out, the banter was better than the first half action.
The chances Chelsea created came courtesy of Oscar, who schemed intelligently in front of United's four-man defence and twice brought good saves out of David de Gea.
United threatened more but with Terry producing a towering performance after shaking Rio Ferdinand's hand prior to kick-off sights of Cech's goal were equally rare.
Robin van Persie should have had a corner when his shot flicked off Branislav Ivanovic, then sent a header over before Tom Cleverley's rising drive was watched on its way by Cech.
It all rather brought the focus back to Mourinho, who gave Moyes a hug prior to kick off but was soon prowling his technical area, often in animated discussion with fourth official Mike Dean.
Only once did he look like erupting though as he strode out, waving his arms furiously after Kevin de Bruyne had been booked for a challenge on Van Persie that left the Chelsea man with a cut lip.
The second period began in much the same unsatisfactory manner.
Terry made an important intervention as United pressed, then Welbeck curled an ambitious effort over before lifing a more delicate attempt just wide from Rooney's short pass.
Amid that flurry of activity around the visitors' goal, Eden Hazard fired goalwards from 30 yards but De Gea barely had to move to make the save.
Both sides had desperate penalty appeals, United when Cleverley's shot struck Frank Lampard on the arm, Chelsea after Ashley Cole hit the deck under pressure from Jones.
In the first instance, Lampard was far too close to Cleverley for Martin Atkinson to award United anything. In the second, Cole was lucky not to get booked for diving, such was the minimal contact which preceded his fall.
The introduction of Torres failed to change much, so Rooney's lung-bursting run back to a corner flag to rob Ramires brought a standing ovation.
It took Rooney some time to get forward after that but when he did, he brought a full length save out of Cech, before delivering the corner that Danny Welbeck should have threatened with rather than screwing a header back where it had come from.
Van Persie had one last shot before an unsatisfactory game was brought to its conclusion.
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