Cook Chicken Mixture:

Chop chicken breasts into small uniform cubes. In a large heavy skillet, warm oil over medium-high heat. Add chicken and taco seasoning; cook for 4-5 minutes, stirring occasionally. Incorporate bell pepper, onion, and garlic; continue cooking for another 5 minutes until chicken is fully cooked. Transfer mixture to a plate and set aside.

Assemble Quesadillas:

In the same skillet, add 1/2 teaspoon oil and place one tortilla. Sprinkle a layer of shredded cheese, then add 1/4 of the chicken mixture, and top with more cheese. Fold the tortilla in half. Cook until each side is golden and crispy. Remove and repeat with remaining tortillas.

Cut and Serve:

For serving: cut each folded tortilla into halves or thirds and accompany with sour cream, salsa, guacamole, or your preferred dipping sauce.