Preheat oven to 350°F. For the Cake, mix cake mix, pudding mix, eggs, water, oil and 1 tablespoon vanilla in large bowl with electric mixer on low speed 30 seconds. Beat on medium speed 2 minutes. Stir in chocolate chips. Pour into greased and floured 12-cup Bundt pan.
Bake 55 minutes or until toothpick inserted in center comes out clean. Cool in pan 10 minutes. Invert cake onto wire rack. Cool completely.
Meanwhile, for the Glaze, mix sugar, milk and butter in small saucepan. Stirring constantly, bring to boil on medium heat and boil 1 minute. Remove from heat. Stir in chocolate chips and 1 teaspoon vanilla until chocolate is melted. Spoon glaze over cooled cake.