Make the marinade – Add the achiote paste, lime juice, orange juice, garlic clove, onion, cilantro, salt, black pepper, and jalapeno into a blender. Add about ¼ cup of water or as needed to help the mixture blend properly.
Marinade the chicken – Cut the chicken thigh into small bite-sized pieces, trimming off the excess fat. In a large bowl, mix the chicken pieces into the marinade and let marinate for at least 30 minutes or overnight.
Prepare the burrito fillings – When you’re ready to cook the chicken, portion out the cheese and cut the avocado. Set aside.
Cook the chicken – Heat a cast iron skillet or grill pan over the stove to medium-high heat. Dry the chicken as much as possible and cook the chicken for about 3-4 minutes on each side, or until fully cooked.
Wrap burrito – Lay the burrito tortilla out on a flat surface, such as a cutting board. Add the chicken pieces into the bottom third of the tortilla. Add the cheese, avocado, a squeeze of lime juice, and salsa verde on top. Tuck the sides of the burrito into a V-shape and continue to tuck and fold until the burrito is fully closed.