If they didn't have the lock on the name before today, Valve certainly does now: Half-Life 3 has been entered in to trademark application with the European Union's Office of Harmonization for the Internal Market, for real. For those of you unfamiliar with the title, Half-Life 3 is a game that's been long-awaited, having seen massive success in its 2nd generation release and seeing so much legendary suggestion behind its release that it in itself has become an event worth waiting for. We've had tips on Half-Life 3 flowing in for years, if you'd like to know, while only the very smallest cross-section of rumors come to fruition. This is one of those times.
What you'll find here is a filing found by an intrepid gamer posting to Neogaf where the board has been slammed with traffic due to an inpouring from Reddit. Valve has not been immediately available for content and, in all likelihood, wont be commenting on this filing at all as such filings aren't normally meant to be seen by the public.
In all likelihood, this filing could be as much a measure of protection for even the most remote possibility of production of Half-Life 3 as it could be a sign that the game is soon approaching. With the dousing of information that's come in the past couple of weeks with SteamOS, Steam Machines, and the new Steam Controller, the hype machine may just be in full force. Any striking of the headlines for Valve is good at the moment, especially when the release of SteamOS is coming on as such an important moment in the overall arch of Valve's history.
You'll also find a ValveTime report turning up what's quite possibly the project tracker file for Half-Life 3 as recent as June. They also found "Episode 3 Movie" which could have to do with the Half-Life or Portal 3 movie spoken about by Gabe Newell and JJ Abrams earlier this year.