Marinate the chicken by mixing lime juice, chili powder, cumin, salt, and pepper in a bowl. Cut the chicken into strips and toss in the marinade. Let sit for at least 15 minutes.
Heat olive oil in a skillet over medium heat. Sauté sliced bell peppers and onions until tender but crisp (about 5 minutes). Remove and set aside.
In the same skillet, cook marinated chicken strips until golden brown and cooked through (6–8 minutes).
To assemble quesadillas, place one tortilla in another skillet over medium heat. Layer half with cheese, then add chicken mixture and more cheese on top. Fold the tortilla.
Cook until golden brown and crispy on each side (about 3 minutes per side).
Slice into wedges and serve hot with salsa or guacamole.
