Whisk together lemon juice, fish sauce, brown sugar, and chiles. Reserve.
Preheat grill or broiler.
Toss 1 tablespoon of the dressing with the chicken. Lay chicken on a cooking spray coated grill rack or broiler pan. Cook 6 minutes per side or until chicken is cooked through. Slice chicken diagonally into thin pieces. Mix chicken, mango, shallots, and ginger and coat with the rest of the dressing. Place salad greens in a serving bowl and top with chicken mixture and mint leaves.