In a large bowl or a resealable plastic bag, whisk together the olive oil, orange juice, lime juice, chopped onion, minced garlic, achiote paste, ground coriander, ground cumin, kosher salt, smoked paprika, dried oregano, black pepper, and chipotle chile pepper until smooth and combined.
Add the chicken thighs to the marinade and turn to coat all pieces evenly; refrigerate and marinate for 4 to 24 hours (do not exceed 12 hours for chicken breasts if using).
Remove the chicken from the refrigerator and let it sit at room temperature for 20–30 minutes before cooking.
To grill: preheat grill to medium-high (about 425–450°F). Clean and grease grates. Place chicken skin-side down first if skin is left on and grill with the lid closed for 5–7 minutes per side, or until an instant-read thermometer inserted into the thickest part registers 175°F for bone-in thighs. Transfer to a cutting board and rest 5 minutes before slicing.
To bake: line a baking sheet with foil and spray or oil lightly. Arrange chicken in a single layer without touching and bake at 400°F for 25–35 minutes, until an instant-read thermometer registers 175°F for bone-in thighs; let rest 5 minutes before serving.
Serve pollo asado with warm tortillas and your choice of sides such as Mexican rice, elotes, or a fruit salsa.