In a medium saucepan, heat milk, cream and butter until just boiling. Whisk in cornmeal in a slow steady stream, stirring until mixture is smooth. Remove from heat and stir in corn kernels and chives. Beat egg yolks and stir into the mixture. Beat egg whites until stiff and fold into the batter to lighten it. Pour mixture into a greased 8 by 8-inch casserole pan, spread evenly with a spatula. Bake 30 minutes in a preheated 350-degree F oven until risen like a souffle.
Spoonbread will be puffed and golden brown; a knife inserted into the center should come out clean.