Make the marinade. In a mixing bowl, whisk together the olive oil, lime juice, white vinegar, chopped chipotle peppers, adobo sauce, garlic, smoked paprika, cumin, oregano, salt, and pepper.
Marinate the chicken. Place the chicken breasts in a large resealable plastic bag and pour the marinade over them. Seal the bag and shake it gently to ensure that the chicken is evenly coated with the marinade. Place the bag in the refrigerator and let the chicken marinate for at least 30 minutes or overnight for maximum flavor.
Preheat the grill. Heat your grill to medium-high heat. If you are using a gas grill, heat it to 375-400F. If you are using a charcoal grill, light the charcoal and let it burn until the coals are white-hot.
Grill the chicken. Remove the chicken from the marinade and discard the remaining marinade. Place the chicken on the grill and cook for 6-8 minutes per side, or until the internal temperature of the chicken reaches 165F. Avoid flipping the chicken too often to retain moisture.
Rest and serve. Remove the chicken from the grill and let it rest for 5-10 minutes before slicing and serving. Serve with your choice of sides like grilled vegetables, salad, or rice.