Preheat oven to 325 degrees F (165 degrees C).
Melt butter with garlic in a microwave-safe glass or ceramic bowl in 30-second intervals, stirring after each melting, for 1 to 3 minutes (depending on your microwave).
Place hoagie roll halves on a baking sheet and brush each with garlic-butter mixture. Divide chicken between each hoagie roll bottom; sprinkle cheese on each hoagie roll top.
Cook in the preheated oven until cheese is melted and bubbling, 10 to 20 minutes. Press top and bottom sandwich portions together.
