Preheat oven to 350º F. Place papers in 24 muffin-tin cups.
In a large bowl, beat the eggs and mayonnaise. Mix in the cake mix, water, and vanilla. Divide the batter among the cups. Bake until a toothpick inserted comes out clean, about 25 minutes. Cool.
For the frosting, melt the chocolate chips in a double boiler; whisk in 1 cup sour cream. Frost the cupcakes immediately.