Place a large pan over medium heat. Drizzle with oil.
Meanwhile, place the oregano, paprika and chilli powder in a large bowl. Add the chopped chicken and lime juice, and mix to coat.
Add the chicken to the pan. Leave to cook for 3 minutes before adding the onion. Cook for a further 2 minutes.
Add the peppers and sauté for 5 minutes, or until softened.
Ensuring the chicken is cooked through, transfer chicken and peppers to a clean bowl.
Place the pan back on medium heat, and drizzle with oil.
Working in batches, place one tortilla at a time into the pan. Top with 3 tablespoons of grated cheese and ¼ of the chicken pepper mixture. Top with another tortilla.
Cook for 2 minutes before flipping. Cook for a further 2 minutes on the other side.
Remove the quesadilla from the pan, and slice into quarters. Allow to cool before serving. Repeat with the remaining tortilla wraps.
Serve with sour cream and smashed avocado for dipping.