Finely mince chile (wear gloves when handling); combine with garlic, green onions, allspice, black pepper and salt. Rub mixture thoroughly on both sides of chicken. Heat oil in a large nonstick skillet over medium-high heat. Cook chicken until no longer pink in center, about 4 minutes per side. Toss together mesclun, carrots and lime juice; divide among 4 plates. Top greens with chicken and serve.