Place parsley, cilantro, garlic, water, vinegar, oil, lemon juice, salt and pepper in bowl of a blender. Blend on high, pulsing, until a smooth sauce is formed; set aside.
Coat a stovetop grill pan with cooking spray. Heat over medium-high heat. Place chicken in pan and grill until cooked through, about 3 to 4 minutes per side; remove from grill pan, cover to keep warm and set aside.
Off heat, recoat grill pan with cooking spray. Place peppers in pan and cook until grill marks show on peppers, about 3 minutes per side. Serve chicken and peppers drizzled with chimichurri sauce.