The Spireites sit 14 points clear of the drop zone with four games remaining in the National League season.
It's largely thanks to a fruitful run under new John Sheridan, whose men are five games unbeaten now.
Sheridan has turned things around with the Spireites staring down the barrel of back-to-back relegations when he returned to the club.
It was the second goalless draw the two sides have played out this season.
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A third clean sheet on the bounce means the Spireites haven’t conceded in 348 minutes of football.
The game started slowly as both sides took a while to get going at in Kent.
The first meaningful chance fell to Jake McKay as he forced hosts’ stopper Lee Worgan into a decent save.
Will Evans was a rock at the back when the Spireites were threatened by the hosts.
Down the other end McKay failed to hit the target after being found by Laurence Maguire.
Spireites’ shot-stopper Joe Anyon watched on as Stuart Lewis lashed an effort wide.
Inih Effiong caused the visitors problems, putting an effort over just before the break.
A neat one-two between Marc-Antoine Fortune and Charlie Carter gave the former a chance to shoot, but he could only fire straight at Worgan.
Just before the hour Alfie Pavey headed over when he should have put Dover ahead.
Mitch Brundle glanced Bobby-Joe Taylor’s free-kick wide as the hosts pushed for an opener.
The Spireites fortunately cleared Kevin Lokko’s header off the line to keep the game goalless.
With 10 minutes left Sheridan’s side should have wrapped up the points.
Fortune was well kept out by Worgan, with Alex Kiwomya firing the rebound over.
Kiwomya and Maguire then both saw efforts blocked as the visitors pushed for a late winner.
Dover: Worgan, Passley, Dove, Lewis, Brundle, Lokko, Taylor, Gomis (Nortey, 86), Reason (Jeffrey, 74), Pavey (Modeste, 70), Effiong.
Unused subs: Walker, Daniel.
Chesterfield: Anyon, Hollis, Evans, Weir, Maguire, Yarney, Reid, Carter (Kiwomya, 75), Shaw (Denton, 75), Fortune, McKay (Barry, 58)
Unused subs: Jalal, Chapman.
Referee: Sam Purkiss