The defeat, the 11th out of their last 12 League outings, will only add to the pressure on manager Keith Curle, whose side have been slipping down the table at an alarming rate in recent weeks.
Chester had their chances but, unlike the visitors, were wasteful in front of goal.
Orient started the game well and almost took the lead inside four minutes when the ball was pin-balling around in the penalty area and Craig Easton finally got the shot in which was bundled off the line by Dave Artell.
It took Chester until the 20th minute to carve out their first effort on goal when a quickly taken free kick sent Michael Branch clear, but the striker lacked conviction and his shot was weak and easily saved by keeper Glyn Garner.
The visitors' pressure paid off 10 minutes before the break when Matthew Lockwood fired home from the spot after keeper Stephane Gillet had felled Paul Connor, as the keeper was fortunate enough to receive only a yellow card for his indiscretion.
Chester started the second half with some new found purpose and had a penalty appeal on 49 minutes turned away when Branch went down in the box.
Stewart Drummond then wasted a great opportunity, shooting over from only six yards out, and Artell volleyed over with the goal at his mercy.
On 58 minutes Chester were unlucky when a Ben Davies shot from the edge of the box struck the post, and Paul Tait inexplicably skied the follow up over the cross bar from around five yards out.
Continued pressure from the home side saw Chester go close on several occasions, but they were hit on the break on 72 minutes when Connor latched on to Gary Alexander's cross with a volley into the bottom corner to seal victory.