Combine tomatoes, onion, lime juice, cilantro,jalapeño, salt and pepper in a small bowl. Set aside.
Preheat 12" Large Skillet on medium heat and add 1 tablespoon olive oil. Add chicken and cook for 3-5 minutes each side, or until juices run clear. Remove chicken from pan and set aside.
Add 1 tablespoon of olive oil to the hot skillet. Add sliced onion and green peppers and sauté until tender. Add minced garlic and sauté another 2 minutes. Add chicken strips and half of the pico de gallo mixture, stir well and keep warm.
Preheat the 11.5" Sauté Skillet and add 1 tablespoon olive oil. Place one tortilla in pan and layer with 1/4 cup shredded cheese, 1/2 the chicken mixture, another 1/4 cup shredded cheese and top with a tortilla.
Flip quesadilla and cook on the opposite side when the bottom tortilla is lightly brown and the cheese has started to melt.
Remove the quesadilla from the pan and cut into quarters. Repeat with remaining ingredients. Serve quesadillas with sour cream and remaining pice de gallo.