Spread 1 tablespoon of pesto sauce on each slice of sourdough bread.
Place the sliced grilled chicken breast on one of the bread slices.
Top the chicken with mozzarella cheese and fresh arugula.
Season lightly with salt and pepper.
Close the sandwich with the other bread slice, pesto side down.
Butter the outside of each slice of bread.
Preheat a skillet over medium heat and grill the sandwich for about 3-4 minutes on each side, or until the bread is golden-brown and the cheese has melted.
Remove from the skillet, slice the sandwich in half, and enjoy your delicious Grilled Chicken Pesto Sandwich!