There shouldn't be any need to remove the DVD drive bay chassis if the PC is built to a common standard.
Remove both sides of the system case.
Detach all cables from the hard drive.
Remove all screws at both sides which hold the drive in the drive bay.
Slide the drive out of it's bay by pulling it towards the back panel of the PC.
You may have to move/hold some cables out of the way whilst doing that.