In a medium bowl, using an electric hand mixer, beat the butter until light and smooth. Beat in the powdered sugar, milk and vanilla until smooth and creamy.
Place the chocolate chips in a small bowl and place over a small pan of barely simmering water. Heat, stirring occasionally, until the chocolate is melted and smooth, about 2 minutes. Remove the pan from the heat. Add the melted chocolate to the vanilla frosting and stir until smooth.