Pico De Gallo: In a small bowl, combine tomatoes, onion, lime juice, coriander, fresh chilli, salt and pepper. Set aside.
Chicken Filling: In a large frying pan, heat 1 tablespoon olive oil. Add chicken and saute until cooked through and juices run clear. Remove chicken from pan and set aside.
Put the remaining 1 tablespoon of olive oil in the hot pan and saute the sliced onion and green capsicum until tender. Stir in the minced garlic and saute until the aroma is strong. Mix in half of the pico de gallo and chicken breast meat. Set aside and keep warm.
To Assemble: In a clean, heavy frying pan, heat one flour tortilla. Spread 4 tablespoons of the grated cheese on the tortilla and top with 1/2 the chicken mixture. Sprinkle another 4 tablespoons cheese over the chicken and top with another tortilla. When bottom tortilla is lightly brown and cheese has started to melt, flip quesadilla and cook on the opposite side.
Remove the quesadilla from the frying pan and cut into quarters. Repeat with the remaining ingredients. Serve quesadillas with sour cream and remaining pico de gallo.