In a medium bowl, combine peaches, cucumber, pepper, and lime juice and set aside.
Preheat grill or grill pan to medium-high heat. With a sharp knife, slice chicken breasts horizontally to yield two cutlets. Sprinkle both sides of with pepper, cumin, and brown sugar, and drizzle with olive oil. Grill chicken for 3 minutes per side or until done.
Stir feta and mint into salsa, spoon over chicken, and serve.
