I roast mine (discovered this way by watching Ina Garten, the Barefoot Contessa, on Food Network. It always leads to moist chicken!
I use boneless/skinless chicken breasts. Brush with a little bit of olive oil on both sides and sprinkle with salt and pepper. Put it on a roasting pan and cover with foil. Bake in a 350 oven for about 25 minutes or so. That's it! It's very moist, slices wonderfully for sandwiches, etc. Good luck!
Chicken breast usually gets dry when it's cooked too long (particularly when you're cooking a whole chicken). Try using a thermometer when you cook to measure internal temperature - that will ensure you aren't cooking it too long.
And as Pookie suggested, poaching is a great method for cooking chicken breast. You can use nearly anything for a poaching liquid - I like to use chicken stock (or just add a cube of bouillon, and some roughly chopped celery, carrots, and onion and a bay leaf to the cooking water. This is all pretty flexible - whatever you want to add to your liquid works as long as you think it will add some nice flavor to your chicken!
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