How do I drill a hole through the center of a cylindrical shaft?

I have a 2 3/8" aluminum round rod. I want to drill a 6mm hole or bore through the rod. The bore must be perfectly centered. I do not have a lathe, but if it's the only way, do they sell them (lathes to work with metal) at Lowe's or Home Depot?

Well aluminum is atleast easier to work with but if perfectly centered is required you would be better off paying a professional but if really close will work, then you got options. First you will need a drill press if not then very carefully with a hand drill, secondly and most important is a vise that will not allow any movement of your stock. always center punch your hole and start small to allow for any error. If your real motivated you can always build a brace for your drill to keep you striaght out of 2x4's.

Depends a bit on how precise you need to be. Get a piece of angle iron (or aluminum), put the shaft in it, and draw or scribe a line on the shaft. Hold the shaft so the line is at the very top of the shaft and drill through it. It will be most accurate if you use a drill press and, of course, a center punch. If you do not have a drill press, you can get pretty close by having an observer stand at one end of the rod and another at ninety degrees and help you line up the drill with the shaft in some sort of depression so that it doesn't roll.
No, neither Lowes nor Home Depot carry lathes.

I would take it to a machine shop. It will be cheaper than buying your own lathe. I would not do it on a drill press, it will not cone out right if you do not have the tools to set it up with. If you take it to a machine shop you need to specify how close to center it needs to be. You can stick the material in a 3 jaw lathe and it may run out a couple grand. The best way to have the hole " dead nuts " in the center is to use a 4 jaw chuck with independant jaws.
Good luck.

Try and find a local machine shop to do it for you. Cheaper than buying a lathe to drill 1 hole. You can use a drill press as well.