What about Halnaker Windmill?
Look south of the track road - paths highlighted off this page: https://www.westsussex.gov.uk/leisure/explore_west_sussex/wildlife_and_landscape/countryside_and_wildlife/places_to_visit/halnaker_windmill.aspx
To find Halnaker Windmill, launch our interactive iMap (http://www2.westsussex.gov.uk/lvmaps/imap.html), select 'British National Grid' from the search menu and enter SU920096 into the search box (top left).
You can see the chalk pit here: https://www.google.co.uk/maps/preview/search/halnaker+windmill/@50.8723521,-0.6921643,914m/data=!3m1!1e3