Danni Francis opened the scoring within the first five minutes with Jane Noble adding a second following an Amy Rook pass.
It was 3-0 when Francis converted a penalty following a foot on the line.
Despite fine defending by Miranda Cooper, Leah Riddy and Olivia Harridine, Chichester hit back twice. But goals from Carol Rutter and a second from Rook sealed a 5-2 victory.
Portsmouth 1sts travelled to third-placed Haslemere in South Central Premier Division 2 with just the bare 11 players due to half-term holidays.
They were further hit by the late withdrawals of Jenny Turvey-Warnes and Katie Spooner.
The hosts scored twice in each half for a 4-0 success.
Megan Cledwyn was awarded the player of the match award as Portsmouth 3rds suffered a 5-0 Division 2 South drubbing against Bournemouth.
There was some determined defending by Andrea Barnes, Amy Durnford and Kathryn Puttock as Portsmouth 4ths were caned 5-0 by Havant 5ths in Division 2 Solent.
Nicky Roch put Portsmouth 5ths ahead in their Division 3 Solent fixture with Gosport Borough 2nds. But that was as good as it got as Borough hit back to win 5-1 despite the efforts of Ruby Grindley, Amelia Munro and Gemma English.