I got a 3.25% refinance, 30 year fixed, from Chase. It's not the 2.875% that another poster reported, but then I've got a coop apartment which is usually a bit higher rate. When I got the loan terms, I saw that 0.6% points had been tacked on to the original closing cost estimate. I complained about this and they took off the points - and let me keep that rate! On its website, Chase is quoting 3.25% with closer to 1% points.
I wasn't aware you could bargain with a big bank, but if your credit & assets look good to the bank it seems that you can. Worth a try. Don't let them make you pay points.