The Rebels were well worthy of the point after coming from behind three times against their Wiltshire opponents.
Slough were under pressure early on, with Andy Sandell having a shot blocked behind for a corner, but the hosts took the lead with 7 minutes played. Sandell broke clear of the last man and crossed in for Chris Allen, who finished past Scott into the bottom corner.
The game flowed from end to end, with James Guthrie denied by Mark Scott, and Charlie Strutton having a shot saved by Kent Kauppinen.
Slough went on to apply pressure on the Chippenham goal, with both Paul Stonehouse and Warren Harris making inroads but having crosses cleared. The Rebels played some of their best football of the season in the final 25 minutes of the half, and the pressure paid off with an equaliser on 37 minutes. Strutton received the ball on the edge of the box, took a step across a defender and fired into the opposite corner of the goal.
Half time arrived with Slough on top, but the Rebels were caught cold two minutes into the second half as Oli Taylor finished past Scott as the ball fell to him in the box.
Slough responded again, and on 58 minutes pulled themselves level. Guy Hollis' long throw into the Chippenham box found its way through to Adrian Sear, whose shot deflected off Scott Harris and into the back of the net.
Again though, Slough's joy was short-lived as Chippenham regained the lead a minute later in fortuitous circumstances. Scott reacted to a header back from Guy Hollis and looked to have gathered the ball, however it squirmed away from his grasp and straight into the path of Sandell, who had a simple tap-in.
Slough piled the pressure on, but the hosts looked threatening on the break. Sandell had another chance to put the game beyond Slough, but he dragged his shot wide of the post after a strong run.
However, Slough equalised for a third time on 76 minutes with a superbly-taken second goal from Strutton. Sear made a great run through midfield and into the penalty area, holding off several defenders. The ball fell to Strutton, who curled it magnificently around Kauppinen on his left foot to draw Slough level once again.
There was still time for both sides to go in search of a winning goal, and Strutton almost completed his hat-trick as he received the ball in the box and took a shot from an angle which came back off the post and into Kauppinen's arms.
Matt Jones' cross almost found the head of Taylor as the ball flew across goal, and Leigh Rumbold almost scored a stunning individual goal after beating two Chippenham defenders, but he curled his shot over the bar.
Late on, Scott had to make a good save to stop Sandell scoring a winning goal, and in the end Slough left with a deserved point after an absorbing 90 minutes of football.
Chippenham Town Line up
Kent Kauppinen, Luke Ballinger, Scott Bevan, Chris Allen, Greg Tindle (c), Mark Preece, Ryan Campbell, Matt Smith, Oli Taylor, Andy Sandell, James Guthrie. Subs: Matt Jones, Iain Harvey, Ashan Holgate, Jon Beeden, Alouine Diouf.