Goals from Miguel Scarlett and – with his third in two games – on-loan Southampton striker Luke Pearce put Borough 2-1 up in the second half but the Essex visitors denied the hosts a win with a late equaliser.
It means Borough remain 11th in the table – four points off the play-off zone.
See pictures by Lydia and Nick Redman on this page and the ones linked, and get the Borough latest in the Herald on Friday.
1. Eastbourne Borough v Chelmsford City pictures by Lydia and Nick Redman (22).jpg
Action from Eastbourne Borough's 2-2 draw with Chelmsford City in National League South at Priory Lane Photo: Lydia and Nick Redman
2. Eastbourne Borough v Chelmsford City pictures by Lydia and Nick Redman (39).jpg
Action from Eastbourne Borough's 2-2 draw with Chelmsford City in National League South at Priory Lane Photo: Lydia and Nick Redman
3. Eastbourne Borough v Chelmsford City pictures by Lydia and Nick Redman (36).jpg
Action from Eastbourne Borough's 2-2 draw with Chelmsford City in National League South at Priory Lane Photo: Lydia and Nick Redman
4. Eastbourne Borough v Chelmsford City pictures by Lydia and Nick Redman (21).jpg
Action from Eastbourne Borough's 2-2 draw with Chelmsford City in National League South at Priory Lane Photo: Lydia and Nick Redman