As a chef I’m always horrified when I see someone placing raw chicken breasts under the grill, or even worse into the oven. When chicken breast is cooked in this manner a lot of moisture will come out of the meat, often resulting in rubber chicken. In truth most domestic grills simply don't get hot enough to cook the chicken successfully.
As with any meat the chicken breasts needs high direct heat at the beginning of the cooking process…to seal in the juices.
The other no-no which helps to create rubber chicken is lack of skin. You see the worst thing Supermarkets ever did was to start selling chicken breasts without the skin. The skin helps to keep the moisture in because it’s a natural protective wrapper. Not only that, chicken skin usually contains a small amount of fat which makes the breast self-basting.
My suggestion to people who don’t like to eat the skin is remove it before serving the chicken…but you will notice a marked improvement in the flavour and moistness on your chicken breast.
LissaT
Pro 
Absolutely true. You can cook buttered skinless chicken breasts wrapped in streaky bacon.