Using a small, sharp knife, cut into the fullest side of each chicken breast making a deep incision into the meat to form a pocket across each breast. Stuff some cheese into each breast then season liberally with pepper and gingerly with salt.
Cut the watermelon into 1/4-inch-thick slices then in large bite-size pieces. Gently slice the tomatoes in a similar shape. If you are using smaller tomatoes, halve or quarter them.
Peel the onion and quarter it lengthwise. Thinly slice the onion and combine with the watermelon, tomatoes, parsley and mint. Dress the salad with lots of salt and pepper and about 1/4 cup EVOO.