The Spireites hit the woodwork through Adi Yussuf and had a goal ruled out in the first-half at the Technique Stadium.
But goalkeeper James Montgomery ensured they claimed at least a point with some good saves after the break.
The draw leaves the Blues in the last play-off spot in seventh with two games remaining against Dagenham and Redbridge and Halifax.
Here are Liam Norcliffe’s player ratings from the game...
The draw leaves the Blues in the last play-off spot in seventh with two games remaining against Dagenham and Redbridge and Halifax.
5. George Carline 6
Certainly not a bad performance. Switched to the left in the second-half. Had a chance to score but headed wide from Mandeville's cross in the second-half. Photo: Andrew Roe/AHPIX LTD
6. Manny Oyeleke 7
Had another good game defensively, breaking up play and keeping the ball. Didn't offer much going forwards though. Photo: jason chadwick
7. Jak McCourt 5
Didn't have his best game but this was his second start in a week after two months out. Replaced on the hour. Photo: Andrew Roe/AHPIX LTD
8. Liam Mandeville 5
Started quite brightly and had some joy playing off the left. But he struggled afterwards and was ineffective. Came off with 10 to go. Photo: jason chadwick