In a mixing bowl, combine the chipotle peppers (remove seeds for less heat), lime juice, orange juice, minced garlic, olive oil, ground cumin, chili powder, paprika, dried oregano, salt, and black pepper.
Butterfly the chicken breasts by slicing them horizontally without cutting them in half, creating a uniform thickness to ensure even cooking. Alternatively, you can pound the chicken breasts to an even thickness.
Place the chicken breasts in the ziplock bag or airtight container and pour the marinade over them. Seal the bag or container and massage the marinade into the chicken. Refrigerate for at least 2 hours or ideally overnight for the flavors to infuse.
Begin preheating your grill or stovetop grill pan by setting it to medium-high heat. Lightly apply oil to the grill grates to prevent sticking.
Remove the marinated chicken from the refrigerator and let it sit at room temperature for about 10 minutes before grilling.
Grill the chicken breasts for approximately 6-8 minutes per side or until they reach an internal temperature of 165°F (75°C) and have nice grill marks.
While grilling, baste the chicken with any remaining marinade using a basting brush.
After the chicken is fully cooked, take it off the grill and allow it to rest for a few minutes before serving.
Garnish with fresh cilantro and serve the Pollo Asado Chipotle with your favorite sides.