It's not possible via *only* HDMI, no. Most capture cards for the PS3 encourage conversion from HDMI to Composite Out instead, because the PS3 is HDCP compliant, so anything over HDMI can't be intercepted, which is what a capture card does.
I have heard the Elgato ( http://www.amazon.com/Elgato-Capture-PlayStation-Recorder-10025010/dp/B00840353W ) is a pretty good one, but because of it's reliance on using Composite Out instead, it only records up to 1080i. Keep in mind, most PS3 games don't output natively at 1080p anyway, so 720p should still be viewable enough. I believe it comes with the cables needed to use with your PS3.