Hmmm, seems like many who passed on lightly disparaging comments failed to
read the fine print.  This fellow is trying to drill through the chromed
bumper.  Now that we've mentioned that salient bit of trivia...the chrome
bumper has a chrome coating, natch, that is pretty damn hard.  Try grinding
a little starting place through the chrome to expose the plain steel
underneath.  The drill should be able to handle the steel.  Use a little
motor oil on the tip of the bit to make things a little easier and preserve
the temper of the bit.

Cheers,

pensioner