The Blues and Dover shared the spoils in adverse weather conditions at the Lookers Vauxhall Stadium.
Ricky Miller opened the scoring, before Ross Hannah cancelled out the opener on the stroke of half time.
The wet and windy conditions were not beneficiary to any side in the opening quarter of an hour; with no real chances created.
Craig Mahon had the first meaningful effort, with an impressive driving run forward, but his shot was the wrong side of Andy Rafferty’s post.
A 30 yard free kick saw John Rooney have the goal in his sights, but the midfielder curled it just wide of the far post.
The Blues were adapting to conditions slightly better than their visitors, Calum Dyson seeing his flick header deflected just beyond the goal.
Dover, flying high in the National League, had a good chance of their own on 36 minutes, but Ben Heneghan made a superb block to deny Sean Raggett from close range.
Nevertheless, the visiting side took the lead with a stunning opening goal just a minute later.
Superb combination play between Nick Deverdics, Ricky Modeste and Stefan Payne teed up Ricky Miller to strike a sumptuous volley beyond Jon Worsnop.
Ross Hannah, who struck his eighth of the season on Saturday, had a chance to equalise with a good turn – but blasted his low, first time shot wide of the mark.
The superb marksman did make it nine for the season on the stroke of half time however, a John Rooney free kick was launched into the box – scrambled towards goal – and found Hannah who tucked home from a matter of yards.
Following a change in referees, Martin Coy limping off, the Blues almost took the lead on the hour mark when Tom Shaw lashed a 25 yard effort goalwards, but was denied by a superb fingertip save from Rafferty.
Miller had a glorious chance to restore the visitors' lead following a slip by Heneghan, but Worsnop made a superb low stop.
The same player had a huge chance to win it with four minutes of normal time remaining - putting a free header wide from a matter of yards - before turning and firing a shot the wrong side of the post.
Chester FC: Worsnop, Higgins, Hunt, Heneghan, Whitmore, Shaw, George, Rooney, Mahon (Chapell 46), Hannah, Dyson (Hobson 67).
Subs Not Used: Forth, Lloyd, Gordon.
Dover: Rafferty, Magri, Raggett, Orlu, Modeste, Miller, Grimes, Deverdics, Parkinson, Thomas, Payne (Ajala 83).
Subs Not Used: Walker, Murphy, Diallo, Sterling.
Scorers: Hannah 45+2; Miller 37.
Referee; Martin Coy.