The 1-0 loss was their fourth straight loss that has cast a large shadow over what had been a bright start under new boss Mark Beard and new owner Simon Leslie.
It leaves them just one place off the foot of the National South table and there is more bad news too – striker Stefan Vukoje has been ruled out for the season after suffering an ACL injury.
See pictures from the Chelmsford game – by Nick and Lydia Redman – on this page and the ones linked and get the Sports latest in the Eastbourne Herald, out on Friday.
1. Chelmsford City v Eastbourne Borough pictures by Lydia and Nick Redman (5).jpg
Action from Eastbourne Borough's defeat at Chelmsford City in National League South Photo: Lydia and Nick Redman
2. Chelmsford City v Eastbourne Borough pictures by Lydia and Nick Redman (1).jpg
Action from Eastbourne Borough's defeat at Chelmsford City in National League South Photo: Lydia and Nick Redman
3. Chelmsford City v Eastbourne Borough pictures by Lydia and Nick Redman (9).jpg
Action from Eastbourne Borough's defeat at Chelmsford City in National League South Photo: Lydia and Nick Redman
4. Chelmsford City v Eastbourne Borough pictures by Lydia and Nick Redman (31).jpg
Action from Eastbourne Borough's defeat at Chelmsford City in National League South Photo: Lydia and Nick Redman