On a baking sheet, toss chicken thighs with olive oil, salt, pepper, and Mexican oregano.
Roast chicken skin side up for 20-25 minutes or until it has an internal temperature of 165 F.
Remove from oven and shred the meat by hand, discarding any skin, bones, and cartilage.
Set aside.
Warm tortillas individually in a pan or good cast-iron skillet over medium heat for 1–2 minutes.
(Alternately, place the tortillas in a stack in the microwave, covered with a damp towel, for 22 seconds on high.)
Then, assemble the tacos, placing the chicken down first in the tortilla, followed by a drizzle of the charred salsa verde, a drizzle of crema, onions, radish, and cilantro.