8-16 oz. boneless skinless chicken breast
cold water to cover
2-3 tsp. salt
1 clove garlic, peeled and smashed
Ensure that all chicken breasts are less than 3/4" thick, either by pounding them or by slicing or butterflying any thick parts of the breast. Place the breasts in a saucepan with a tight fitting lid. Cover with cold water and add the salt and garlic. You could also add wine or lemon juice, onions, celery, lemongrass, herbs or spices. Bring the liquid just to a boil--as soon as you see large bubbles coming up, turn the heat off and place the lid on the pot. Allow to sit for 15 minutes undisturbed.
The chicken will be cooked through but still very moist and tender. You can store the chicken in the poaching liquid or use the liquid for cooking. The chicken is great in recipes such as chicken salad, enchiladas, in noodle soup, with cheese on toast, etc...
This same technique can be used for fish, but I don't know how long to leave it sitting. I would assume only 5-8 minutes.
Joe's thoughts on poaching a whole bird:This technique is actually excellent with an entire bird as well, especially when combined with a shock in cold liquid. Generally, the shocking step is highly recommended, as it relaxes the muscle fibers, further inhibiting moisture loss. You can then very gently re-warm the meat to serving temp, without further cooking it.
In chinese cookery, the chicken is plunged into boiling water and shocked in cold several times in order to gradually and evenly cook it through; almost a poach-braise. White rice is subsequently prepared with the chickeny poaching water. Combine with piquant condiments such as XO sauce and chile paste for some of the best white food ever.
Also: the above is for so-called "white" poached chicken. "Red" chicken calls for tinting the poaching liquid with soy, and usually xiaoxing (aka Shaoxing) wine, for the element of acidity described in the original post (although I am unfamiliar with the definition of poaching which requires acidity?).