The chime is not there simply to sound nice, it actually serves an important purpose. It indicates to the user that the computer has passed all the motherboard and ram tests which run every time you boot. If something is wrong, you will not hear a chime, or on older computers, you will hear a death chime.
I usually recommend people keep their speakers at least on very very low volume so you can still tell whether the chime is playing or not. For example, if you have a computer that makes fan and hard disk noises, but shows no video, it makes it easier if you can hear the chime so you know its not a problem with the motherboard, but rather another component like the video card.
If you leave your computer muted for every boot, then you will have more of a hassle determining the problem since there is no easy way to change the volume without being in the OS.