John Terry went close with a header and Chelsea twice hit the woodwork, but City’s Martin Olsson also had a strong penalty appeal turned down.
The draw means Chelsea’s title hopes can be ended by a Liverpool win at Crystal Palace on Monday.
Norwich must beat Arsenal and hope Sunderland lose their last two games.
Victory would have moved Chelsea top, but a draw means Jose Mourinho’s side are a point behind leaders Manchester City and second-placed Liverpool, having played a game more than both.
The Portuguese has long since made his desire for a new striker known and his case for summer recruits was strengthened by a toothless performance that was only partially improved by the introduction of Eden Hazard’s inventiveness in the second half.
Norwich ended a run of eight successive away league defeats and a thumbs-up to the fans from stand-in manager Neil Adams at the final whistle suggests the Canaries still believe, but their chances of survival are very slim.