In top of double boiler, mix 1/3 cup granulated sugar, the cornstarch and 1/8 teaspoon salt. Gradually add milk, stirring with wire whisk until blended. Cook over simmering water, stirring constantly, until mixture thickens and coats the back of a metal spoon, about 10 minutes. Remove from heat. Add chocolate chips, 1 tablespoon butter and the vanilla; stir until smooth. Pour pudding into bowl; cover surface directly with plastic wrap to prevent skin from forming. Cool 30 minutes.