Heat covered pan to med-low heat. Add just enough oil to cover the bottom of the pan and chicken. Keep covered and cook, only flipping once until each side is cooked. Remove chicken and shred. Set aside and allow to cool.
In the same pan add diced onion and cook uncovered until translucent, but not brown. Remove onion and allow to cool.
Wipe pan clean and reduce heat to low.
Scatter chicken, shredded cheese, onion and coriander over one tortilla and top with the second. Place quesadilla into the pan and cover. Cook until lightly browned on one side, flip over and brown the other side.