Shred the cooked chicken (or thinly slice it) - you can do it either in the food processor or by hand.
Put the chicken in a microwave-safe bowl and cook for 1 minute, or until warm.
Assemble the quesadillas: put tortilla on a plate. Sprinkle shredded cheese over 1/2 of the tortilla (the part with the cheese should look like a semicircle). Put the shredded chicken over the cheese. Put more shredded cheese over the chicken. Fold the empty side of the tortilla over the cheese.
Heat the oil in a non-stick frying pan over medium high heat (I like to use the griddle or 2 frying pans on 2 burners to save time).
Put the assembled quesadillas on a frying pan (as many as you can fit in a single layer).
Cook for 1 minute, or until the bottom is golden-brown.
Carefully flip the chicken quesadillas and cook on the other side for 1 minute, or until golden brown.