Staining a fence?

Hello, the previous owner of my house had stain the fence about 5 years ago so it's due for a new stain. I'm planning on going with the restore-a-deck brand.

My only concern is this: what are the regulations for staining the sides of my fence exposed to my neighbor's backyard? They don't have any fence, so is it as simple as just mentioning it to them and walking over to their property to do the staining work? Is it up to the neighbor to even allow me to do that? I'd think I'd have to strip the old stain down so the use of chemicals would be involved while I'm in their backyard stripping the side of my fence exposed to them.

Please help me know the answer to this. Thanks!