Heat first 4 ingredients in a heavy saucepan over medium-high heat 6 to 8 minutes (do not boil). Remove from heat. (Mixture will curdle.)
Combine cornmeal and Parmesan cheese in a large bowl. Pour milk mixture over cornmeal mixture, whisking until smooth. Let stand 30 minutes or until lukewarm. Stir in baking powder and baking soda.
Beat egg yolks lightly, and stir into cornmeal mixture. Fold in chives.
Beat egg whites, sugar, and salt at high speed with an electric mixer until stiff peaks form. Carefully fold into cornmeal mixture.
Pour into a buttered 13- x 9-inch baking dish.
Bake at 350° for 30 minutes or until top is golden and a wooden pick inserted in center comes out clean. Serve spoonbread immediately.