According to actor Jim Beaver (via his Twitter feed), Supernatural begins shooting it's first episode tomorrow, with actor Jensen Ackles directing.
"In Vancouver. SPN season 6 starts tomorrow with episode 4 (!) w/Jensen Ackles directing. I WON'T tweet details, so don't ask! It's great!
We're doing #4 first because a director needs a week of prep b4 an episode, & Jensen can only get that week by going first.
This season will be the first season creator Eric Kripke won't have his hands in the day-to-day events of Supernatural, a position he gave up to his right hand, Sera Gamble, at the end of season 5.