Welcome to the forums!
First, tell us about this 351 and transmission you have. Is it a 351W or 351C? How about the transmission? Manual or automatic?
My first thoughts: If this is a 351W it can fit, although it is a tight squeeze between the very narrow shocktowers of the '66 ('67 and later were further apart), as the block has a 9.2" deck, about an inch taller than the 289/302 blocks (If I remember correctly). There are a lot of issues with the swap, but it is not impossible and there are even specialty parts on the market now specifically for this swap.
If the engine is a 351C, then it will probably be much more hassle than it is worth. You are likely going to run into so many problems and do so much fabrication that it will not be worth it; a big pig C6 isn't going to fit into the skinny transmission tunnel, etc.
So I offer you this: If you already have a 289 or 302, stroke that puppy out to 347 and save yourself a world of headache. Conversely, if you do go with a 351 swap, the only reason it would be worth it is to take advantage of the extra cubes, in which case you better stroke that motor out to make it worth it.