Have you looked at the Chichester record office catalogue?
Wills in West Sussex Record Office says
The following are available within the Record Office:
Original wills for the archdeaconry of Chichester, and the peculiar jurisdictions within it, up to 1858, together with those for the Chichester District Probate Registry, which covered most of West Sussex, up to 1928.
Microfilm copies of wills for the archdeaconry of Lewes, 1518-1858, the Archbishops Peculiar of South Malling 1588-1858 and Royal Peculiar of Battle 1531-1616, 1657-1730.
Microfiche for all the main series of pre-1858 probate records, and microfilm for probate records 1858-1900 - readers are asked to use them to save wear and tear on the originals.
Original wills from 1900-1928 for Chichester District Probate Registry.