Put the first six ingredients in a ziploc bag and squish around to combine. Add the chicken breasts and toss them around to make sure they are even coated with the marinade. Refrigerate for up to 4 hours.
Preheat grill to high. Spray grill rack with a little cooking spray or mop with oil (whatever method you use to help foods not stick to your grill). Grill breasts about 5 minutes on each side or until cooked thoroughly. Start testing on second side after about 3 minutes. Grill to 160-165.
Remove chicken from grill and let rest (covered with foil) for 5-10 minutes.
Combine the watermelon, mango, onion, cilantro, pepper, lime juice, sugar and salt in a bowl. Toss to make sure it is well combined (this can be done a day ahead of time).
Serve chicken topped with salsa.
Video
Notes
Can use boneless skinless thighs for this. Use fresh lime juice, not bottled, for the best flavor.