Combine shredded chicken, buffalo wing sauce, and blue cheese in a small bowl.
Preheat a small skillet over medium heat.
Spread 1/2 tablespoon butter on one side of a slice of bread. Place bread butter-side-down onto the skillet bottom and place pepper Jack cheese on top. Top with chicken mixture. Butter a second slice of bread with remaining butter on one side and place on top of sandwich, butter-side-up.
Cook sandwich in skillet until lightly browned bread and flip over; about 2 1/2 minutes per side.