Chicken breasts are naturally very lean, which means when they are overcooked by even a little bit, they get very dry. But it is imperative to be sure they are cooked enough—anything below an internal temperature of 160 degrees has a good chance of causing potentially serious food borne illness.
The solution is simple: to ensure your chicken is tender and moist—and safe!—use an instant-read meat thermometer. It must be inserted at least one inch into the meat, with the tip at the thickest part of the center (and not touching the bone). Since a boneless chicken breast is nowhere near an inch thick, you need to insert the thermometer horizontally.