City keeper John Danby was the hero with a string of superb saves to deny a County side who put them under the cosh throughout the second half despite already having one eye on the play-offs.
Substitute Adam Proudlock turned well on the ball just inside the box only to see his effort blocked by the legs of Danby three minutes after the interval.
And four minutes later Proudlock again was in on goal only for his low effort to be blocked by the onrushing keeper.
County skipper Gareth Owen headed an effort wide and Gary Dicker also nodded over the bar while Chester also survived strong claims for a penalty after Proudlock appeared to be brought down by Paul Linwood after 67 minutes.
Proudlock also shot into the side netting, and with eight minutes remaining Danby produced an unbelievable save to deny a point-blank header from Anthony Pilkington to ensure Chester picked up the point that they desperately needed.