I need drill a 3/8" diameter hole in my chainsaw bar to attach a plate on it.
I sincerely doubt that you should be custom hacking something onto your chainsaw bar. If this was a legitimate attachment that is provided by the chain saw manufacturer then there should already be mount points defined and instructions provided for installing such option.
Custom modifications to a tool, especially one that is already as dangerous as a chainsaw, should not be done because of the additional danger and risk to safety that can come into play.
dont listen to these other guys. i have done the same thing with one of my saws to build a portable sawmill with it.
because the bar is hardened, use this great trick (can be used on any hardened item). get yourself a set of carbide masonry bits. grind the carbide teeth on the end of the bits (they come usually with a double bevel for masonry percussion drilling) to match the type of cutting edge on a normal drill bit (more like a chisels cutting edge), just not quite as acute of an angle. then start drilling, slowly and with lots of water for cooling. once the hole is through, move up to the next size.
most carbide inserts on drill bits are c3 carbide and top out at about 68 on the c scale. so you can drill anything that is softer than that. your bar is only around 50 - 55 on the c scale, so it will work fine.