Eddie Smith saw an early effort tipped over by goalkeeper Kent Kauppinen, but the visitors were on the front foot, and a superb tackle from Billy Jeffreys was required to stop a dangerous cross from the right.
Perhaps against the run of play, Slough took the lead on 20 minutes with Smith again the man on target. Billy Jeffreys got his head to a long throw in, and the ball deflected to Smith, whose left-footed volley found the bottom corner, his eleventh goal of the season.
Jamie McClurg had a great chance to extend the lead, but blasted wide from the edge of the box after Kauppinen had punched the ball away – and Slough then had a huge let-off when Mark Francis saw a shot cannon back off the crossbar after the Rebels had given the ball away.
Slough then doubled their lead on 37 minutes. A free kick was played short to McClurg, who took aim from 20 yards and found the back of the net via a slight deflection off Jon Beeden, with Kauppinen wrong-footed.
With the two goal lead, Slough went on to end the first half playing confident, attractive football, but the second half was a different story, with Chippenham racing out of the blocks, determined to pull a goal back as soon as possible.
Francis cut in from the left and saw a shot deflected over, and Luke Ballinger dragged a shot well wide, before McClurg served notice that Slough were still a threat with a fierce strike which rebounded back off the post.
On the hour mark, Chippenham reduced the deficit to just one. Good play from James Guthrie on the right was rewarded as his ball across found Jordan Roberts in space, and the striker side footed past Jake Somerville through a crowd of players.
Minutes later, Francis raced clear but put his shot straight at the Slough stopper, with Jeffreys able to hack the ball away.
Slough responded with a double substitution, Leigh Rumbold and Johnnie Dyer replacing Scott Harris and Adrian Sear, but minutes later, the visitors drew level. Agonisingly, the ball was allowed to roll all the way across the face of goal and Guthrie arrived at the back post to score from a tight angle.
Chippenham went on to look the more likely to take all three points, and Beeden shot over the bar from a good position late on, but the game finished all square and Slough's unbeaten league run was extended to six matches.
Chippenham Town Line up
Kent Kauppinen, Connor McCormack, Jon Beeden, Bryan Smith, Greg Tindle (c), Mark Preece, Alex Ferguson, Mark Francis, Jordan Roberts, Luke Ballinger, James Guthrie. Subs: Toby Osman, Matt Coupe, Michael Pook, Iain Harvey, Alan Griffin.