Oil the fillets and season with fajita seasoning. Griddle for 2 minutes on each side. Remove from the griddle and pop the peppers in the same pan. Grill for 2 minutes and remove.
Slice the chicken. Pop a tortilla on the griddle. Top one side with cheese, then chicken, peppers, avocado and more cheese. Flip the taco over to 'close' it, then grill the other side to melt the cheese.