Chicken Fajitas with Savoy Cabbage Slaw

Name: Chicken Fajitas with Savoy Cabbage Slaw
Ingredients: 4 Tbs. olive oil, plus more as needed; 2 tsp. chili powder; 1 tsp. crumbled dried oregano; 1 1/4 lb. boneless, skinless chicken breasts; 2 large red onions, halved and sliced lengthwise; Coarse kosher salt and freshly ground pepper, to taste; 8 to 12 small flour or corn tortillas, each about 6 inches in diameter; 1/2 small head savoy cabbage, halved, cored and thinly sliced; 1/4 cup chopped fresh cilantro; 2 Tbs. fresh lime juice; 1 large avocado, pitted, peeled and sliced