Marinate the chicken and grill until cooked through. This step can be done a day ahead to speed up dinner.
Slice the cooked chicken into long thin strips.
Preheat a pan or electric griddle to 350 degrees.
Spread margarine evenly on one side of each tortilla and place 1 (or 2) tortillas margarine side down on the heated skillet.
Spread evenly with shredded cheese, then top with sliced chicken and a little more cheese.
Finally, top with another tortilla, margarine side up. Carefully flip over to cook both sides until lightly browned.
Remove from skillet and continue with remaining tortillas until all quesadillas are cooked.
Cut into quarters for serving.