Chichester was the son of Colonel John Chichester of Arlington Court, Barnstaple. He served in the Royal Navy. Chichester became High Sheriff of Cardiganshire in 1831 when he was living at Llanbadarn Fawr.
He held the seat until 1841.
He was created a baronet in 1840. Chichester died at the age of 57.
Chichester married Caroline Thistlethwayte. Their son Alexander inherited the baronetcy.