Heat a non-stick skillet over medium heat and lightly coat with cooking spray or butter.
Place one flour tortilla in the skillet.
Spread half of the shredded Monterey Jack cheese evenly over the tortilla.
Evenly distribute the shredded chicken and black beans on top of the cheese.
Sprinkle the remaining Monterey Jack cheese over the chicken and beans.
Cover with the second flour tortilla.
Cook until the bottom tortilla is golden brown and the cheese is melted, about 3-4 minutes.
Carefully flip the quesadilla using a spatula, and cook the other side until golden brown, about 2-3 minutes.
Remove from the skillet and let it cool for a minute before cutting into wedges.
Pack in a lunchbox with a side of salsa or sour cream for dipping.