Here is all the info you could possibly want to know about the latest rumors on this seemingly non-existent episode.
http://half-life.wikia.com/wiki/Half..._Episode_Three
The following is just the last entry into the log linked above.
A T-shirt, worn by a Valve employee, that led to rumors concerning Half-Life 3's announcement
On Thursday, December 1st, Chandana Ekanayake, part of Seattle-based game developer Uber Entertainment, saw a Valve employee wishing to remain anonymous, wearing a t-shirt saying "Half-Life 3", with an icon similar to the Half-Life 2 logo. The employee apparently "knew as much about Half-Life 3 as we do, which is absolutely nothing." [33]. Marc Laidlaw confirmed that "the T-shirt was real", but refused to comment further. [34]
On December 9th, an anonymous US-based voice actor revealed thay had recorded lines for "Half Life: Episode 3" (sic). This, combined with the then-recent previous event, leads to rumors that the next Half-Life game will be revealed at the 2011 Spike Video Game Awards on December 10th. [35] However, this did not occur.