Cooking raw chicken beside heating quesadillas
Of course you can.  The question is whether it is a good idea or not in terms of food safety.

What you don't want to have happen is for raw chicken juices to splatter onto the quesadilla, especially after it has been flipped so that the side where the juices splatter will not be cooked again.

In actual practice, you have to assess the risks:


How much juice will splatter, and how far?
Will the quesadilla still be hot enough (or be turned) to kill any pathogens anyway?
Will enough settle on the quesadilla to have any significant chance of being a real risk?   (The risk of infection increases with the quantity of pathogens present.)


In practice, unless you are serving at-risk populations like the immune-compromised, elderly, or very young children, the risk is probably quite low as long as the foods are far enough apart that the juice is not flowing from the chicken to the quesadilla.

In a professional food service environment, you probably should not do this; at home, you must assess your own tolerance for risk.