Preheat the oven to 400°F. Rub the chicken with 1 tbsp olive oil, 1 tbsp oregano, salt and pepper to taste, and bake in the oven for 30 minutes, until browned and cooked through.
Prepare the slaw by thinly slicing the cabbage, fennel, celery, and radishes. To make the dressing, mix together the lemon juice, 2 tbsp olive oil, Dijon mustard, and season with salt and pepper. Add the dressing to the salad, toss well, and allow to rest before serving.
Prepare the yogurt dip by combining the cucumber, yogurt, mint, and 1 tsp oregano. Serve alongside the finished dish.