1. Place a chicken breast between two sheets of plastic wrap and use a meat pounder or heavy skillet to flatten it into a 1/2-inch-thick paillard. Place the pounded chicken on a large plate or plater and repeat with the remaining chicken breasts. Drizzle the chicken with one tablespoon of olive oil, turning to coat the breasts on both sides, then sprinkle the chicken on all sides with one teaspoon of the salt. 

2. In a medium bowl, combine the melon, scallions, mango, ginger, chile (if using), parsley, citrus juice, and remaining three tablespoons olive oil and half teaspoon salt. Gently stir in avocado.

3. Prepare a gas or charcoal grill to high heat. Dip a folded paper towel into the vegetable oil and use tongs to grease the grill greates. Place the chicken on the gril and cook until it has grill marks, two to three minutes. Turn the chicken over and grill on the other side until the chicken is cooked through, about two minutes longer. Transfer to a platter. (If cooking indoors, just replicate this process in a skillet. The chicken will be deeply golden brown on both sides and no longer pink or tranluscent in the center. 

4. Serve the salsa over the chicken. 

**Tip: Any kind of seasonal fruit works in the salsa -- you can use pineapple, peaches, plums, or nectarines, in place of the mango or melon if you like.