Place chicken on a heated grill. Coat one side with barbecue sauce.
Wrap potatoes in foil and pierce with a fork. Toss onto the grill with the chicken.
Cook chicken for about 5-7 minutes, then turn over.
Slice zucchini and yellow squash in half, lengthwise. Drizzle with olive oil and season with salt and pepper; place onto grill and cook for approximately 5 minutes, flipping once.
Baste other side of chicken with barbecue sauce and cook 5 more minutes or until chicken is cooked through. (If it is a thinner piece of chicken, this time should be reduced). Check potatoes by squeezing. If they are soft, they are done.
Serve chicken with potatoes, watermelon and veggies.