We know Half Life 3 has long fallen under the spectre of vaporware, but the way this rumor has been sourced gives it some level of credibility, so we'll share the details for now and leave it to you to judge if it's real or not.
Niels Boch of NoShitShurlock claims he has been in long email correspondence with developer John Guthrie for a while now, an Guthrie has finally admitted that the game is coming next year. More than that, the game is being planned for release on Windows, Mac, Xbox 360, Playstation 3, Playstation 4 and Xbox One.
Guthrie did not divulge exactly how far gone they are in development, but that they will have a trailer and demo ready in time for E3 2014, when Valve intends to return to the convention after such a long absence.
Half Life 3 will start where the last game left off, and the old cast of characters, with Gordon Freeman and Alyx Vance is coming back. Guthrie explains that they decided to switch gears from making a Half Life 2 Episode 3 since they've come up with a different story for this one. Other factors that prompted production of the game is the dawn of the 8th generation of consoles, and Valve's own efforts upgrading Source, as well as improving game mechanics. Guthrie concludes that the game will again be a solid single player experience without multiplayer.
As a reminder, way back in 2006 Gabe Newell was referring to Half Life Episodes 1 and 2 as effectively Half Life 3. His reasoning was they had designed the episodes as a way to push forward the Half Life storyline, but reusing and mastering the same assets and tools they had used in the older games, to more efficiently deliver product to consumers. As he put it, although they decided not to name it so, the episodes were effectively what they intended to be Episode 3.
Of course, that's all changed now, and given that Half Life 2 did come out at onset of the 7th generation, to eventually release on Xbox 360 and PS3, it definitely sounds possible that Valve has been planning and developing this secretly for months. It's definitely still on the rumor mill for now, but rumors are starting to sound more credible and even likely.
Image is from Half Life 2.
Source: NoShitShurlock