In a medium mixing bowl combine the olive oil, juice and zest of the lime and lemon, garlic, and all seasonings. Pour into a zip top bag. Remove excess fat from your chicken thighs and place them in the bag. Squish them around so they are coated in the marinade. Zip the bag, and refrigerate for at least 3 hours or up to 8 hours.
While the chicken is marinating, make the salsa verde cream. Combine the salsa verde, sour cream or crema, cilantro, and juice of 1 lime in a blender and blend until the cilantro is in small pieces. Pour into an airtight container and refrigerate until cold. *The flavors are best after sitting in the fridge for 24 hours, in my opinion.
Heat griddle on medium heat until it reaches about 400℉. *See notes for skillet cooking instructions.
Place the chicken on the heated griddle and cook untouched on the first side for about 4-5 minutes. When you place the chicken on the griddle, be sure to press down gently so that the entire thigh is in contact with the cooking surface. After 4-5 minutes, flip the chicken thighs to the second side and continue to cook untouched for an additional 4-5 minutes, or until the internal temperature of the thighs reaches 165℉. *Cooking times may vary based on the size of the chicken thighs and the griddle temp.
Transfer chicken to a cutting board and let rest for 5 minutes before slicing into bite-sized pieces.
While chicken is resting, warm the tortillas on the griddle. Then wrap the warmed tortillas in a kitchen towel to keep them soft and pliable.
Assemble your chicken street tacos. Add some of the chicken on top of the warm tortillas. Top with a spoonful of pico de gallo, a sprinkle of red onion and cotija cheese, and drizzle with the salsa verde crema. Squeeze a small lime wedge over the top, if desired.