The draw probably flattered Steve Tisdale's men who were outfought by a dogged Chester team who ended their six-game losing streak and halted their alarming slide down the table.
Ryan Lowe and Ritchie Partridge had great chances to score for Chester but the draw was probably a fair result in the end.
Chester's Partridge had the first attempt on goal in the eighth minute but his shot drifted narrowly wide of the target.
Exeter's top scorer Adam Stansfield looked the most likely to break the deadlock in the first half and on 35 minutes it was his sharp turn and shot which tested Chester keeper John Danby for the first time.
Three minutes later Exeter keeper Paul Jones did well to deny Partridge with a smart block after the Chester striker had robbed the hesitant Steve Tully in his own box. Ryan Lowe blasted the rebound wide when he should have at least hit the target.
Exeter began to exert some control early in the second half but it was Chester who went closest just after the hour mark when Lowe was played through on goal but somehow hooked his shot wide from just eight yards with only the keeper to beat.