Barnet recorded their fourth draw on the trot but in turn ended the league leaders' run of six wins, as a scrappy encounter at Underhill ended goalless.
Few would have predicted the scoreline prior to the game, which featured the Conference's two leading scorers in Giuliano Grazioli and Daryl Clare but chances were premium and the few that did arrive fell foul of some wasteful finishing.
A feisty opening half saw little by way of quality as the two teams struggled to cope with the swirling wind, while a succession of stoppages did little to improve the flow.
Chester had the first strike on goal, but Alex Smith's shot from distance flew high and wide. Ben Strevens then threatened for Barnet, racing down the right before feeding Grazioli who, from the edge of the box, had his low shot deflected wide.
The standard of football early on belied the team's lofty league positions - fouls rather than shots were the order of the day.
After seeing Barnet's two efforts from the edge of the area blocked, the visitors broke swiftly through Darryn Stamp on 37 minutes.
The striker beat three players and set up substitute Chris Lane, who duly rifled in the finish but it was ruled out for offside.
Ismail Yakabu then fired wide for the hosts before the half's best chance fell in injury time to Stamp, whose miscue was indicative of much of the play.
Shortly after, Smith fizzed a left-sided centre across the face of goal, but from Danny Williams' lay-off Stamp fluffed his effort well wide.
Barnet got a slice of goal early in the second goal when, from Ian Hendon's near-post cross, the waiting Grazioli volleyed narrowly wide.
Then Hendon's free-kick only struck the defensive wall where Liam Hatch was waiting, but his weak effort was comfortably collected by the keeper.
As the game progressed, Barnet began to play the majority of the pressure, though Chester fashioned the clearest chance on 66 minutes.
Lane found Clare in acres of space inside the Barnet area, but despite taking an age to line up his shot, the forward fired well wide.
Strevens then let rip from 25 yards and was unfortunate to see his sweet strike fly over.
Minutes later, the midfielder burst into the area and only a superb low save by Iain Turner prevented what would have been the winning goal.
As the game belatedly sprung to life, Clare seemed poised to get on the end of a measured throughball for the visitors, but the alert keeper, Ademola Bankole arrived at the ball first, picking up a knock for his troubles.
It was then Danny Maddix's turn to frustrate Chester with a brave last-ditch tackle to deny substitute Michael Twiss, who dragged a shot wide ten minutes later.