Is it safe to defrost chicken in the fridge with cold water and leave it overnight?

Safest way to do it! Other ways would be to defrost in the microwave (quickest, but not my personal favorite), or just run it submerged under cold water until it is the way you want it. As long as it stays under 39F (4C), which it will under cold running water... but that's kind of a waste of water, if you can help it. According to the Ontario Food Handler's Certification Handbook, all ways are acceptable, but time permitting, I'd suggest the fridge.