Don't gift one share of stock. It will be more of a pain than it is worth for the recipient for taxes and if they decide to sell the fees would probably eat up any gain.
Several years ago we purchased one share of Disney. My husband located a source that framed it and everything. It was a christmas gift for his sister, this isn't something that's going to be turned in, more of an art piece maybe. I'd have to ask him if he remembers where he got it. If you're interested, let me know. However, I'm not sure if was a source for only Disney or if they did that for other corporations.