In a game of few chances, a lack of a cutting edge made it a third consecutive draw and left Mark Wright's struggling side still in the relegation zone.
The visitors came into the game with their own run of poor form, having lost their last four matches, but they went close on 12 minutes when Michael Boulding hit a left-foot shot from a difficult angle which keeper John Danby saved at the near post.
For the home side, Jay Harris hit an effort from distance which was easily claimed by Rhys Evans.
In the 17th minute Evans found a Kevin Ellison shot hard to handle but managed to snatch up the ball at the second attempt as Ryan Lowe looked to capitalise on the initial fumble.
A minute later, Paul Mullin forced a save from Danby with a header at the far post which looked destined for the bottom corner until the keeper palmed it away at full stretch.
Ten minutes before the interval Boulding struck an effort which Danby did well to save, and at the other end Lowe's curling effort from the edge of the box was tipped around the post by Evans.
Luke O'Brien rifled a shot from distance just over the bar in the opening stages of the second period.
Chester went close on 56 minutes when Lowe hit a good effort from 18 yards out that Evans saved with a great stop to his right.
And two minutes later they were again denied when Ritchie Partridge looked odds on to score when the ball was played to him just six yards from goal, but Zesh Rehman produced a superb last-ditch block to prevent the winger from scoring and ensure the points were shared.