Marinate the chicken in the oil, lime juice, chili powder, cumin, oregano, garlic, salt and pepper in the fridge for 30 minutes to a few hours.Grill the chicken over medium-high heat until cooked, about 2-3 minutes per side. (Reserve the marinade.)
Heat the oil in a pan.
Saute the onions until tender, about 5-7 minutes.
Add the peppers and the remaining marinade and saute until the peppers are tender, about 5-7 minutes.Melt a touch of butter in a pan over medium heat.
Place a tortilla into the pan, swirl it around in the butter.
Sprinkle half of the cheese over half of the tortilla followed by 1/2 cup of the chicken fajitas, 1 tablespoon salsa, the remaining cheese and finally fold over the tortilla.Cook until the quesadilla is golden brown on both sides and the cheese is melted, about 2-4 minutes per side.