Layer the grilled chicken strips and cheese onto 2 slices of bread. Assemble the sandwiches and lightly butter both sides.
In a medium non-stick pan over medium-high heat, grill the sandwiches for 2 to 3 minutes, until the bottom is golden brown. Flip and continue to grill until the cheese is melted.
Remove from heat and allow the sandwich to cool to room temperature before slicing in half and packing inside a lunch container.