Chrome can supposedly support 32779 characters in the address bar[0], and a legal chess game should not exceed more than ~5900 moves, due to the 50 move rule. That will be enough to encode any valid game if you don't need to support IE.
Interesting. According to that stackoverflow, Chrome is one of the shortest URL lengths of the modern browsers (firefox/safari/chrome). However, it also notes you have to take CDNs and web servers and search engines into consideration, so the ginormous length limits of safari and firefox probably won't be useful any time soon.
[0]: https://stackoverflow.com/questions/417142/what-is-the-maxim...