A first competitive Chippenham goal for Nat Jarvis was enough to earn the three points on a very dry and dusty pitch that made passing football very difficult.
Jarvis was first to threaten either goal when his sixth minute shot was blocked.
Later, Jack Compton’s fizzing cross saw a deft header from James Guthrie go straight into keeper Jack Turner’s grateful arms.
Slough’s first opening arrived after Scott Davies fired a free kick into the Bluebirds wall and the loose ball found its way to Chris Flood, who steered his shot off target.
The best chance of the half came four minutes before the interval when Chippenham keeper Will Puddy was quickly off his line to block Sam Togwell’s shot. The Rebels defender chipped the ball back in to the back post area, and Ben Harris met the ball with his head, only to see the ball come back off the post.
After the break Ben Harris was again in the thick of the action, first firing wide from a free kick before his looping header was comfortably saved by Puddy.
Just past the hour mark, Compton’s free kick was blocked and the ball fell to George Rigg 30 yards out – but his looping shot was easily gathered by Turner.
For Slough, Sam Togwell then headed over from a Davies corner but it was a Chippenham corner which led to the crucial moment of the game.
On 68 minutes Turner punched the corner delivery clear, but the ball was returned low into the danger zone, where Jarvis swivelled and fired home.
Two minutes later, with Slough looking for a quick reply, George Wells saw a long-range drive saved by Puddy. But Slough could easily have been two behind almost immediately following that chance, as Karnell Chambers – who was clean through on goal - dragged his shot wide from eight yards.
Flood connected with a low cross from Louie Soares on 78 minutes, but Puddy saved again, whilst Mark Nisbet tried his luck from distance but saw his effort sail over.
Wells fired another effort over and Simon Dunn was also thwarted as Chippenham stood firm to hold on to their clean sheet and a first win of the season.
Chippenham Town Line up
Will Puddy, George Rigg, Curtis McDonald, Kieran Parselle (Alex Ferguson 73) Greg Tindle, Will Richards, Josh Smile, James Guthrie, Nat Jarvis, Karnell Chambers, Jack Compton (Andy Sandell 68). Unused substitutes: Matt Smith, Dean Evans, Nick McCootie.