To make the salsa, bring a medium-size saucepan of water to boil over high heat. Drop in the peaches and cook for 30 seconds. Using a slotted spoon, submerge the peaches into a bowl of ice cold water to cool. Remove and drain on paper towels. Using a sharp paring knife, peel the peaches, remove the pit, and cut into 1/4-inch dice. In a medium bowl combine the peaches and the remaining ingredients, and using a rubber spatula, gently fold to combine. Taste for seasoning, cover, and chill.
Pre-heat an outdoor grill to medium high. Lightly coat with oil.
Season both sides of the chicken with salt and pepper, drizzle lime juice over and add a dash of cumin. Grill the fillets until no longer pink, 2 to 3 minutes per side. Transfer to a clean plate, and set aside. Top with the salsa and serve.