Hi There
Just came across your post while researching my own family. My great grandfather Watson Elliott owned the Chestnuts. I think the official address is Union Street although it stood on the corner where that road joined Timbrell Street. Watson lived here from at least 1911 until his death in 1933. So who was your ancestor? Watson's son William dies in 1917 - is that him? If so we are related, though somewhat distantly. I have the whole tree on Ancestry so am happy to send you an invite to view if you are interested.
To clear up any misunderstandings - there is now a modern Registry Office called "the Chestnuts" in Trowbridge but it's nowhere near and nothing to do with the house called the Chestnuts. That was sold we think when Watson died and was later owned by the brewery Ushers. It was demolished in the 1960s but I can remember being taken to see it as a child.
Regards Mandy