Liz, can you tell me if this is from his birth certificate or from a census "place of birth"?
People tend to put their birthplace down wrong on censuses.
I have to say that I've lived in the area most of my life, and don't know of it, (although I'm an "old map" nut)
The Kitchers are a really old Forest family, some of whom were charcoal burners/woodsmen in the middle of nowhere.
I'm thinking it *could * be "Rhinefield"
which is an area of the Forest, not sure if it would have come under Fawley Parish though