Dartford's National League South play-off hopes were left in the balance on Saturday.
The Darts are now five games without a win after Chippenham staged a smash and grab raid at Princes Park.
It leaves Dartford outside the play-off places with just three matches of the season remaining.
Darts started with Tom Murphy up top alongside Darren McQueen while Elliot Bradbrook was in the back four and Jordan Wynter in central midfield.
Those plans were disrupted within the first 20 minutes when injury forced Bradbrook off and Andre Coker came on down the left wing with Wynter dropping back into defence.
Dartford's first attempt at goal came on 21 minutes when Tom Murphy took aim from 20 yards and his low shot was comfortably saved by keeper Will Puddy.
Murphy headed wide from a Dan Johnson cross seven minutes later.
Chippenham, without a win in their previous six matches, put five across the back and never threatened at the other end. They played a short corner only to be caught offside and then a shot free-kick on the edge of the Darts penalty area was blocked en route to the danger area.
After a slow start to the second half, Dartford created some good chances. On the hour mark, Ben Greenhalgh's 30-yard left-foot effort was tipped over by Puddy.
Greenhalgh then headed straight at the keeper from Hayes' delivery before Lee Noble was unable to direct his header from Coker's cross on target.
The biggest cheer of the afternoon came with 16 minutes left when Andy Pugh replaced Murphy - his first outing since a double-leg break in July.
He almost scored with his first touch but within four minutes Darts were behind when keeper Bailey Vose - a spectator throughout - was beaten to the ball by Kieran Chambers and Adriel George was left with the simple task of scoring into an empty net.
Dartford: Vose, Driver, Wynter, Bonner, Greenhalgh, Noble, Murphy (Pugh 74mins), McQueen, Bradbrook (Coker 18mins), Hayes, Johnson. Subs not used: Wells, Smith, Leveson.
Chippenham: Puddy, Rigg, Davies, Rutty, Tindle, Ossai (Chambers 62mins), Jarvis (George 74mins), Parselle, Evans, McCootie, Smile. Subs not used: Gunner, Ferguson, Horgan.