The result did little to ease their relegation worries, but they did keep only their second clean sheet of the season.
However, Chesterfield, who were on the back foot for much of the game, finished strongly and had two glorious late chances to snatch maximum points.
Orient controlled most of the first half but failed to test the Spireites' keeper Barry Roche with all eight efforts missing the target.
The home side's best chance fell to striker Lee Steele after just nine minutes when Wayne Corden threaded a ball in from the left, but the forward fired wastefully over.
Home skipper John Mackie then headed a corner over the bar from the edge of the area before debutant Peter Till, on loan from Birmingham, tried his luck from distance but his snapshot flew over the bar.
Little was seen of Chesterfield as an attacking force but, on 33 minutes, Kevan Hurst went close with their first real effort, a speculative lob from the right.
The visitors carved out their best chance of the half minutes later when Hurst crossed from the right and veteran striker Wayne Allison's header from six yards out was tipped away by Orient keeper Glyn Garner.
After the interval, the game followed a similar pattern and Corden's 25-yard free-kick on 52 minutes was tipped away by keeper Roche, Orient's first effort on target.
After that Corden lobbed a shot just wide before Roche pulled off a great save to keep out Jabo Ibehre's close-range header.
The O's continued to press as Steele and Till went close to breaking the deadlock. Chesterfield were growing in stature though and Mark Allott set the alarm bells ringing when he shot just wide with 73 minutes gone.
The Spireites finished with a bang and Colin Larkin should have netted but was denied on 76 minutes by Garner's excellent save.
Then Paul Hall frittered away a glorious chance to steel the points.
Larkin thought he'd won the game in the last minute when he lobbed home, but the effort was ruled out for offside.