Put the chicken breasts in a glass baking dish.

In a small bowl, combine the lime juice, garlic, olive oil, oregano, cumin, salt and chili powder. Whisk until well blended. Pour the mixture over the chicken, turning the chicken so it is well coated. cover the bowl with plastic wrap and place in refrigerator for 1-3 hours.

Adjust the broiler rack in your oven so the heat will be 4-6 inches from the top of the broiler pan. Turn the broiler on high.

With tongs, remove the chicken from the marinade and place on the rack with the broiler pan. Discard the marinade. Broker the chicken until it is lightly browned on top, 5-7 minutes. Turn the pieces over with tongs. Continue broiling the chicken until it I'd completely cooked through and browned on the second side, 5-7 minutes longer.

Wrap the tortillas in foil, set aside; turn the broiler off. Using pot holders, carefully remove the broiler pan from the oven. With tongs, transfer the chicken to a cutting board.

Turn the oven on 400°F Fahrenheit. Warm the tortillas in the oven for 5-10 minutes.

Put your fajitas together and enjoy.