Since FEAR 3 is not being handled by Monolith Productions I have zero inside info. I'm really not sure how I feel about it being put out by Day 1 instead of Monolith Productions.
Switching studios never really seems to pan out for games but we can hope they don't change the feel of the FEAR universe to much.
Here's a link to the ING page that has the teaser:
http://ps3.ign.com/dor/objects/45905/fear-3/videos/fear3_trl_announcementtrailer_4710.html Since the video was already posted here I didn't embed it.
Anyway the main website is the same and you should totally check it out in all of it's creepy-ness!
http://www.whatisfear.com/ ((PS: the pregnant thing is freaking me out))
I'm sure most of you have already read this but here's a link to the 'Monolith hearts Day 1' post
http://www.lith.com/Studio/News/April-2010/ANNOUNCING-F-E-A-R--3,-FROM-DAY-1-STUDIOS