I don't know if you have gotten this problem fix yet, but my 08 LS is doing the same thing. I've checked pretty much everything and found that the noise is coming from inside the transmission. I think it's just the output shaft bearing. I've had this same issue with my old Honda CRX I had. I'm taking mine to the dealer as its still under warranty.

 

edit: seems the 2010 wheel bearings are still covered.

https://www.chevyhhr.net/forums/show...t=22231&page=2