Shiloh Remy gave Danny Bloor’s team the lead in the first half but Joe Parker levelled for the Wiltshire hosts nine minutes from time.
It leaves the Sports in 11th spot but only three points off the play-off zone with six games to play – starting at Weymouth on Saturday.
See pictures from Chippenham v Borough game by Lydia and Nick Redman on this page and the ones linked. Get the Borough latest in the Eastbourne Herald every Friday.
1. Chippenham v Eastbourne Borough pictures by Lydia and Nick Redman (6).jpg
Action from Eastbourne Borough's 1-1 draw at Chippenham in National League South Photo: Lydia and Nick Redman
2. Chippenham v Eastbourne Borough pictures by Lydia and Nick Redman (36).jpg
Action from Eastbourne Borough's 1-1 draw at Chippenham in National League South Photo: Trevor Round:Lydia and Nick Redman
3. Chippenham v Eastbourne Borough pictures by Lydia and Nick Redman (24).jpg
Action from Eastbourne Borough's 1-1 draw at Chippenham in National League South Photo: Lydia and Nick Redman
4. Chippenham v Eastbourne Borough pictures by Lydia and Nick Redman (14).jpg
Action from Eastbourne Borough's 1-1 draw at Chippenham in National League South Photo: Lydia and Nick Redman