Line a 9-in. square pan with foil; grease foil with 1 teaspoon butter and set aside. In a small heavy saucepan, combine 1 cup sugar, 2/3 cup corn syrup and water. Bring to a boil over medium heat, stirring constantly. Reduce heat to medium-low. Cook, without stirring, until a candy thermometer reads 250°-266° (hard-ball stage).
Meanwhile, beat egg whites in a heat-proof large bowl until stiff peaks form. With mixer running on high speed, carefully add hot syrup in a slow steady stream, beating constantly at high speed until thickened; cover and set aside.
In a large heavy saucepan, combine remaining sugar and corn syrup. Bring to a boil over medium heat, stirring constantly. Reduce heat to medium-low; cook, without stirring, until a candy thermometer reads 275° (soft-crack stage).
Meanwhile, melt remaining butter. Pour hot syrup into reserved egg white mixture; stir with a wooden spoon. Stir in the walnuts, vanilla and melted butter.
Pour half of nougat mixture into prepared pan; press evenly. Sprinkle with chocolate chips. Tint remaining nougat mixture with red and/or green food coloring if desired; spread over chocolate chips. Press down evenly with buttered fingers. Let stand for several hours until set.
Using a knife coated with cooking spray, cut nougat into 1-in. squares. Wrap in plastic or waxed paper if desired. Store at room temperature.