Heat a skillet or large pan over a medium flame. Cook pork chorizo and white onion until soft and crumbly, approximately 10 minutes.
Warm up refried beans in a pot and 8 tortillas on the comal. Keep the tortillas in a tortillero or inside a cloth kitchen towel to keep them warm.
Take 4 tortillas and evenly spread on top of each, one layer each of refried beans, chicken, chorizo, jalapeños, black olives and Four Quesos blend. Cover each quesadilla with one of the remaining 4 tortillas.
One by one cook both sides of the quesadilla on the comal until it is crisp and the cheese has melted. Remove from heat and cut into quarters.
Serve with Crema Mexicana and guacamole, if you wish.