The only Hannah Chater I can find of around that period was born in 1845 at Napton on the Hill in Warwickshire, daughter of Henry and Hannah Chater.
I think though you have had some good responses from members of the Chater family who have all supplied you with solid family information, that is factual. It seems strange to me that there is no trail to Hannah Chater and Thomas Holloway since around 1645ish.
I give up after a night of searching, but am pleased to have read so much about my relatives that have been given to you in various posts.
Cheers and God Bless,
Miss Chater