My Cat Is White With Green Eyes, What's The Chance Of Him Being Deaf?

If your cat can hear well now, then most likely your cat will not become deaf when it gets older.

White cats with green eyes do not normally have any hearing problems; it's the white cats with BLUE eyes that do.  Different genes can cause white coat color in cats, and the gene that is responsible for blue-eyed white cats is a "lethal dominant" gene, unlike most genes for white, which are recessive.  The dominant white gene carries with it a gene that causes the microscopic hair cells inside the inner ear, which transmit sound vibrations into nerve impulses that are picked up by the brain, to not develop properly, if the cat gets a white gene from each parent, and this results in a deaf or partially-deaf cat.  The white coat associated with green or gold eyes is a different gene, so those cats usually can hear normally.