Preheat the skillet or electric griddle over medium high heat. Spray with nonstick cooking spray, or melt some butter onto the grilling surface.
Butter the outsides of the bread, and spread mayo on the insides of the bread.
Assemble sandwiches with shredded chicken, shredded white cheddar and shredded mild cheddar. Grill until golden on both sides, flipping carefully, about 1-2 minutes per side.
Repeat until all sandwiches are grilled.
Serve BBQ Chicken White Cheddar Grilled Cheese with simple side salad.