Pat the chicken pieces dry. Sprinkle with the oregano and season with salt and pepper. In a large skillet, heat the oil over medium-high heat. Add the chicken and cook, turning occasionally, until just cooked through, about 5 minutes.
Add the hominy, broth, cilantro and chipotles and bring to a simmer. Cook for 1 minute. Spoon into bowls and top with the lettuce and radishes.