In a large skillet, heat the olive oil over medium-high heat.
Add the diced onion and bell pepper to the skillet and sauté for 2-3 minutes, until the vegetables are tender.
Add the shredded chicken to the skillet and stir to combine with the vegetables. Cook for an additional 2-3 minutes, until the chicken is heated through.
Lay one of the flour tortillas flat on a clean surface. Sprinkle half of the shredded cheese evenly over the tortilla.
Spoon the chicken and vegetable mixture on top of the cheese, spreading it evenly over the tortilla.
Sprinkle the remaining cheese on top of the chicken mixture.
Place the second flour tortilla on top of the cheese, pressing down gently to adhere.
Carefully transfer the quesadilla to the skillet and cook for 2-3 minutes on each side, until the cheese is melted and the tortilla is golden brown.
Remove the quesadilla from the skillet and let it cool for a minute or two.
Cut the quesadilla into wedges and serve with sour cream, salsa, and/or guacamole, if desired.