In a small mixing bowl add the crab meat, 3 tablespoons of the mayonnaise, onion, celery, chives and Old Bay Seasoning. Gently combine.
Evenly spread remaining mayonnaise on one side of each slice of bread. Heat a large skillet or griddle over medium-low heat. Add butter and allow to melt.
Divide half the cheese evenly on top of the bread slices. Spread the crab salad over the bread followed by the remaining cheese. Top each with a second slice of bread, mayo-side up. Transfer the sandwiches to the pan with a spatula.
When the underside is golden brown, about 3 minutes, use a spatula to flip the sandwich and continue to cook. Gently press down on the sandwich to encourage browning and continue to cook until the cheese has melted and the underside is golden brown, about an additional 3 minutes.
Remove the melts to plates and cut in half. Serve hot.