Place the desired amount of tortillas on a flat surface and spread 1/3 cup bean mixture over half of each tortilla. Top each with 1/4 cup chicken and 1/4 cup cheese. Fold each tortilla in half to cover filling.
Add butter to a large skillet; heat over medium heat and place 2 quesadillas side- by-side in skillet. Cook 5 minutes, turning once, or until golden brown on each side and cheese melts. Repeat with remaining quesadillas.