It was the second successive home game that Orient have had to settle for a point in a goalless draw as their slide continued.
In a poor first half it was the O's who created the better chances and they almost went ahead on nine minutes.
On-loan striker Andy Barcham raced onto Wayne Corden's clever pass but Gillingham goalkeeper Simon Royce parried his first shot before the young striker fired the rebound against a post.
There was no fluency to the game, but Royce was the busiest of the two keepers and make a smart stop to deny John Melligan when he cut in from the right and shot from distance.
Barcham was Orient's most lethal threat and, after Corden and Adam Boyd combined, the young striker fired over from 25 yards.
Then, just before the break, Corden almost gave Orient the lead but his shot was deflected over the bar.
After the interval the match became a much better spectacle as Gillingham were more of an attacking force.
Indeed, Orient goalkeeper Stuart Nelson emerged as the star, making several excellent saves. First he denied the impressive Adam Miller who had raced cleaned through.
Then he made two impressive late stops from Andrew Crofts as the visitors threatened to grab a winner.
But Orient had their moments too as Paul Terry headed a Corden corner over the top.
Orient's best second-half effort fell to Barcham who was denied by the impressive Royce. Then the Gillingham keeper also kept out Orient substitute Jason Demetriou's effort.
When top scorer Boyd finally tucked the ball into the net the effort was ruled out for offside - which just about summed up Orient's day.