If the breast is thicker than 3/4 inch, place it on a cutting board that is lined with plastic wrap. Add another piece of wrap on top of the breast. Pound the breast with a meat mallet to 1/2 to 3/4 inch thin. Coat the breast completely with EVOO. Season all sides with chili powder, salt, and pepper. Set aside while you prepare the grill.
Preheat your Foreman grill on high with the top closed for approximately 5 minutes.
Place the chicken on the grill and close the top. Grill for 4 to 5 minutes or until juices run clear. Check with a digital meat thermometer. You are looking for an internal temperature of at least 165°F.
Remove the chicken to a cutting board and allow it to rest while you prepare the pico de gallo. In a medium bowl, combine the tomato, jalapeno, scallion, cilantro, lime, salt, and pepper.
Slice the chicken thinly. Brush EVOO on one face of each tortilla. Turn 2 tortillas over so the oiled face is down. Place 1/2 of the cheese on two of the tortillas. Add the chicken equally divided to each tortilla. Spoon the pico de gallo equally on top of the chicken. Top with the remaining cheese. Place another tortilla, unoiled face down, on top of the cheese.
Grill each assembled quesadilla with the top closed for 5 minutes or until the cheese has melted and there are golden grill marks. You might have to do this one at a time, depending on the size of your Foreman grill.
Remove the grilled quesadillas to a clean cutting board and cut into 4 equal triangles. Serve immediately while still warm with plenty of napkins and previously prepared side dishes.