In a blender, combine the brown sugar, vinegar, olive oil, lemon juice, garlic, mustard, lime juice, Worcestershire sauce and lime zest. Blend until smooth. Arrange the chicken breasts in a large nonreactive dish and pour the marinade on top. Let stand at room temperature for up to 1 hour, turning occasionally.
Light a grill or heat a grill pan. Remove the chicken from the marinade. Season the chicken with salt and pepper and grill until browned and cooked through, about 3 minutes per side. Serve hot or at room temperature.