No breed of chicken is entirely quiet, but there are several that make hardly any audible fuss at all. This only applies to the hens, though - cockerels will always crow, no matter what breed you have.
The more docile breeds are the quietest ones. Bantams tend to match their smaller size with smaller voices.

A Rhode Island Red hen
Amongst the breeds reckoned to be the quietest are:
- Ameraucana
- Australorp
- Brahma
- Buff Orpington
- Cochin
- Java
- Nankin Bantam
- Plymouth Rock Bantam
- Rhode Island Red
- Rosecomb Bantam
- Sebright Bantam
- Wyandotte