For the tortillas, mix cornmeal with flour, salt and water in a bowl. Knead until a moist, soft dough forms. Cover bowl and let rest for about 15 minutes.
Divide prepared dough into 4 portions, roll out into thin circular tortillas with a rolling pin. Toast each side in a dry skillet for 1/2 to 1 minute. Fry tortillas until light brown spots show and then keep warm.
For the filling, rinse wax peppers, trim, cut in half, remove seeds and cut into strips. Peel onion and chop. Rinse tomatoes and dice. Peel avocados, remove pit, dice and mix with lime juice. Rinse parsley, shake dry, pluck leaves from stem and cut into strips.
Season chicken breast fillets with salt, pepper and cayenne pepper.
Heat 2 tablespoons oil in a frying pan and fry chicken breasts for about 8 minutes on each side until golden brown. Remove from pan and keep warm in the oven.
Saute wax peppers in remaining hot oil for about 6 minutes. Simmer and season with salt and pepper. Add tomatoes and parsley and saute for 1 minute. Then mix in avocados and season with salt, pepper and cayenne pepper. Remove chicken from the oven, cut into strips and add back into pan.
To serve, fill tortillas with vegetables and chicken meat.