The startup chime you hear is at the hardware level, not the software level. It is similar to the beep any pc makes when starting.
It is a signal that the hardware is OK.
Somewhere along the line, some one said "why does it have to be a beep?" and the mac startup chime was born.
So yes, it is normal for you to hear the startup chime even when you are running X. You will hear it alot less, since you'll never have a crash!
FaRuvius