Panic has posted a blog post taking claim to having created the world's first Emoji domain, see http://www.panic.com/blog/2011/07/the-worlds-first-emoji-domain/
. Emoji is a set of mappings to icons that are commonly used on Japanese mobile phones but have since migrated into usage on iPhones, etc. With the release of Max OS X Lion, apparently they are baked into Apple's latest operating system too.
The actual domain is 💩.la, or as encoded, http://xn--ls8h.la/
However, it is actually not legal according to the IDN specification. The codepoint is U+1F4A9 which according to RFC 5892 is Disallowed. I know the post gives ICANN all the credit for disallowing it in most registries, but a prudent registry would not be handing out domains that are invalid and only work in some software because they haven't fully implemented the IETF standard.