Combine the lime juice, chilli powder, oregano, cumin and black pepper in a bowl.
Add the chicken, onions, red pepper and green pepper to the lime mixture and stir to coat. Let stand for 15 minutes.
Preheat a barbecue for medium-high heat.
Oil the barbecue grate, or use an oiled barbecue basket. Barbecue the chicken and vegetables until deeply browned, about 7 minutes. Place on a cutting board, and chop the chicken and vegetables into 1cm strips.
Serve in the tortillas with the lettuce, coriander, tomato and soured cream. Serve pico de gallo or salsa on the side, if liked.
Pico de gallo, a fresh salsa of jalapenos, onion and tomato is typically served with fajitas. Try this recipe - it's delicious!