Cobblers had the best of the early stages but found it difficult to create chances and their only real opening fell to Luke Guttridge, who shot over when well placed.
At the other end, Craig Westcarr turned well in the penalty area but saw his effort saved by Lee Nicholls.
Chesterfield came into the game as the half progressed and created two good chances in as many minutes. Former Cobbler Sam Togwell broke from midfield before firing over and moments later Sam Hird headed straight at Nicholls.
Top scorer Jack Lester came closest to breaking the deadlock either side of half-time when he struck the crossbar just before the break and was then just off target after the restart. In between, Nicholls went close for Cobblers when he was denied by goalkeeper Richard O'Donnell.
Those chances apart, neither side did enough to win it in the second half but it was the visitors who were the happiest with the point as they extended their unbeaten run to seven league games.