In a rare goalless encounter at the Emirates, the home side had the better of the match - Laurent Koscielny hit the post and a subdued Robin van Persie missed some good chances - but Chelsea defended resolutely and deserved a point.
There was bad news for Arsenal and England after winger Walcott limped off in the second half. Manager Arsene Wenger later confirmed he had a "serious hamstring" injury and was expected to miss three weeks.
The result puts Arsenal on 65 points, six clear of the chasing pack with four matches remaining as they close in on third place; Chelsea stay sixth with 58 points, with qualification for next season’s Champions League looking increasingly dependent on winning it in May.
The first half started slowly, a cagey affair as Arsenal patiently worked openings while Chelsea - who had made eight changes from the 1-0 win over Barcelona with Tuesday’s Champions League semi-final second leg in mind - looked for the break.
One such move saw Salomon Kalou burst into the area the left, and the Ivorian was too honest when Bacary Sagna came across him with a clumsy challenge: it looked like a foul but Kalou tried to stay on his feet and the chance was gone.
Arsenal, meanwhile, went close when Van Persie put wide when Walcott’s superb free-kick found him unmarked at the far post: it had come to him quickly, but the Dutchman should have used his right and not his preferred left.
Down the other end Chelsea had their first chance, from a corner as Gary Cahill blasted over from a position where he often scores.
That was midway through the half, and the relative lack of opportunity frustrating the home fans as a lull followed., which lasted until just before half-time when the match finally sparked into life.
Koscielny - who had a fine game - headed against the bar with an inventive reverse header after a Van Persie free-kick found him unmarked, a theme that was mirrored down the other end when John Terry - culpable a minute before - headed over after the French defender lost his man.
Arsenal had another chance before the break as Petr Cech made himself big to keep out Van Persie’s blasted finish, the Dutchman’s first touch on the chest killing Alex Song’s high pass and allowing him a rasping effort that the Chelsea keeper did well to get away.
There was a bit more pace about the early stages of the second half, with Chelsea looking livelier than before and the quiet Fernando Torres denied by an inch-perfect Koscielny tackle.
The Spain striker also had a penalty appeal waved away, going down under pressure from Alex Song, as Chelsea cranked up the pressure.
Down the other end Van Persie was cutting an increasingly frustrated figure, earning himself a booking for a wild challenge on Michael Essien as he struggled to get into the game.
And, while it had started well, the half soon lost its fizz, degenerating into a bitty affair punctuated by fouls and bookings as neither goalkeeper was really tested.
Both sides made changes, Chelsea bringing Juan Mata into the fray in the hope that he would be able to complete the final pass that his team-mates lacked, while Arsenal lost Walcott to an apparent foot or ankle injury, Gervinho bright in his place.
One of Arsenal’s subs, Abou Diaby, had a low effort blocked after some fine interplay between Van Persie and Gervinho, while Van Persie had a penalty appeal waved away after a tussle with Gary Cahill.
Van Persie has gone off the boil in recent weeks and he drew a blank again, wasteful in smashing wide with his weaker right foot after a slip from Terry, before inexplicably delaying his finish after getting the better of Cahill late on.
In a fairly frantic finish there was a late scare for the Gunners when Thomas Vermaelen’s slip let Daniel Sturridge in; Koscielny’s last-gasp challenge nicked the ball clear.
Arsenal responded by piling on some late pressure but they continued to flounder at the last, unable to force Cech into meaningful action.
Chelsea, meanwhile, had their own attacking problems with as Torres toiled badly at the end, but a draw was a decent result in the circumstances and fuel to their ambitions of shutting out Barca in midweek.