Talk about doing more. While the entire chicken is delicious enough to throw on the grill. There are a few cuts that come highly recommended. Chicken breasts are perfect for anyone watching out for their weight. However, this cut can dry out quite quickly. To avoid this, use butter in the marinade. The drumsticks and thighs pair perfectly with a delicious BBQ sauce. These are the juiciest cuts of chicken that remain moist after grilling.