Make the marinade: In a blender or medium bowl, combine the achiote paste, orange juice, lime juice, minced garlic, vinegar, oregano, cumin, salt, pepper, and smoked paprika (if using). Whisk or blend until the achiote paste is completely smooth. Whisk in the olive oil.
Marinate the chicken: Place the chicken thighs in a large bowl or a resealable plastic bag. Pour the marinade over the chicken and turn to coat thoroughly. Seal and refrigerate for at least 2 hours, but ideally 4-6 hours for the best flavor.
Preheat the grill: When ready to cook, preheat your grill (or a cast-iron skillet) to medium-high heat. Clean and oil the grates well.
Grill the chicken: Remove the chicken from the marinade, letting the excess drip off. Discard the remaining marinade. Place the chicken on the hot grill and cook for 5-7 minutes per side, without moving it for the first few minutes to develop a good sear. The chicken is done when it registers 165°F (74°C) on an instant-read thermometer.
Rest and slice: Transfer the cooked chicken to a cutting board and let it rest for 5-10 minutes. This is crucial for juicy meat. After resting, chop the chicken into bite-sized pieces.
Warm the tortillas: While the chicken rests, warm the corn tortillas on the grill, in a dry skillet, or in the microwave.
Assemble: Serve the chopped pollo asado on the warm tortillas. Top with onion, cilantro, a squeeze of fresh lime, and your favorite salsa. Enjoy immediately!