How to quickly and safely defrost chicken?
I suppose that depends on what you're defrosting it for.
The microwave (on low power) is safe and quick. The downside is that you're using a microwave, which means there's a good chance you'll actually cook the outside slightly in the process, and you're killing enzymes that are normally part of the flavour. The lower the heat, the less the impact of this, but it's still a problem. If I'm preparing the meat for marinating, stir-fry, etc., something with a powerful or thick sauce, then I wouldn't worry about it, but if it's going onto a grill with just a little bit of seasoning, you might want to avoid this.
Running it under warm water would seem to work, but I've found that it takes forever to defrost this way (the exterior will loosen up but the interior stays stubbornly frozen), and you're soaking it in the process. This really isn't suitable if you need to pound or fold the meat or do anything complicated with it.
I would use the microwave if desperate, but it's really best to thaw the meat in the refrigerator or, if you're in a bit of a hurry, the sink. It takes longer, but it'll turn out much better than the microwave in terms of flavour and tenderness.
P.S. One other word of advice: If you're making a dish that requires the chicken to be cut or sliced, it's best not to defrost it all the way. It's easier to cut when frozen, and will defrost very quickly once it's in pieces. I'm mainly talking about the breast here, this doesn't work so well with meat stuck to bones.
Update: I'm noticing a lot of recent hubbub about the dangers of defrosting in the sink / on the countertop or using warm water and I wanted to clarify something. Please note that that the advice above applies to chicken that will be immediately cooked after defrosting and that the defrosting is done over a period shorter than 2 hours.
Raw chicken must not be kept at any temperature above 40° F (4.4° C) for more than an hour or so. Do not defrost a chicken breast in the sink and then toss it back in the fridge. Definitely don't try to defrost a whole bird this way - stick to the refrigerator or very cold running water.
As long as you follow the above precautions and cook the chicken thoroughly (up to an internal temperature of 165° F), you're not in any serious danger of salmonella poisoning, even if the original piece of meat was contaminated - and most chicken sold today is contaminated, for the record.
If the meat is going back in the refrigerator for marinating or you plan to delay cooking for any other reason, then you need to either thaw it very fast (using the microwave) or at a very low temperature (using the refrigerator or cold running water).