It is 52-06-08 ∇ 18:23:47, Lunar Standard Time. Or at least, it was when this page loaded. You can see the real time clock in the menu section of this page.
If you just googled in here, then you might think just that. Information on the first you'll on the following page that answers the question "What is Lunar Standard Time?". The second question isn't as straight forward. The concept of Lunar Standard Time isn't new of course. It has been around in various forms ever since the idea of colonizing the Moon entered the minds of Sci-Fi writers. You can however find out who we are and what LunarClock.org is all about, by reading about us.