Although the source cannot be confirmed, a post on reddit appearing to be an email exchange between a hopeful fan and Valve director Gabe Newell seems to be the first acknowledgement of Half-Life 2: Episode 3 in a good while. In the email exchange, which can be seen here, the fan in question writes a haiku:
Do you like haikus?
I like to write them sometimes…
Episode 3 soon?
To which Gabe Newell responded:
Haikus are neato
They have a rigid structure
Episode 3 ships in
While fairly cryptic, the haiku (if legitimate) seems to be a good sign of health for the long-awaited conclusion to the Half-Life 2 story. Details on the game have been very slim, and it has been nearly 4 years since the release of its predecessor.