Chances were few and far between and the result leaves Aldershot two points above the drop zone while Chesterfield's play-off hopes look to be fading.
The Shots, under new boss Andy Scott, were quicker to the ball in the first half and Craig Reid, Danny Rose and Danny Hylton all went close in the opening 20 minutes.
Reid forced Tommy Lee into another diving save in the 43rd minute but Chesterfield improved after the break and both Jordan Clark and Neal Trotman saw efforts saved by Jamie Young.
Trotman then saw a header drift narrowly wide before Jack Lester fired into the side-netting while, at the other end, Peter Vincenti had a shot deflected just wide.
Both teams could have won it in the closing minutes with Marc Richards denied by Young before Sonny Bradley met a Rose corner but his header was cleared off the line by substitute Danny Whitaker.