Yeah Poker, he actually might have to remove it. I have that EXACT SAME CASE and I have mine removed. My cooling is just fine. I like the look of it better with it off anyways haha. I actually think the side fans made the dang airflow screw-y anyways...it messed up the flow from front -> back by pushing and pulling air from the side. In my case (no pun intended
), I had to remove the bar to make room for my aftermarket VF1000 for my 3870, so the little bars (and the housing even after removing the bars) were pushing on the copper heatsink fins when closing the case--that's a no no! Anywho, I only use one PCIe slot so I had room at the bottom of my case to remove all unnecessary slot covers and jimmy-rig an 80mm fan to exhaust the heat (flowing down from my vid card) out the back of my case..but this may not work in your case because I think the 4870 is a dual slot card, whereas mine is a single. However, being that yours is a dual slot means that it already exhausts the fan heat out the back out of one of the PCI expansion slots...sooooo you should be good.
Haha that was a long explanation.
Just remove the bar. You'll be fine
EDIT: Also, btw, thought I should add that the blue fan insert is removable so if you can get the black bar to fit without the blue fan enclosure (simply snaps out), then you can leave the bar in, it just won't snap into place, but the case will hold it there just fine.