In a blender, combine the white vinegar, pineapple juice, lime juice, achiote paste, adobo sauce, morita pepper, garlic, oregano, cumin, smoked paprika, black pepper, and salt. Blend until smooth.
Place the chicken thighs in a large ziplock bag or a non-reactive container, and pour the marinade over the chicken. Ensure the chicken is well-coated, then seal the bag or cover the container. Refrigerate for at least 2 hours, or overnight for best results.
Preheat a grill or grill pan to medium-high heat (375 to 400°F). Remove the chicken from the marinade, allowing any excess to drip off. Brush the grill or grill pan with vegetable oil to prevent sticking.
Grill the chicken for 5 to 6 minutes per side, or until the internal temperature reaches 165°F (74°C) and the chicken is cooked through.
Allow the chicken to rest for a few minutes before slicing it into thin strips.
Serve the Chicken Al Pastor in tacos, burritos, or bowls with your favorite accompaniments.