Preheat the oven to 350 F. In a large bowl, mix together cake mix, eggs and vegetable oil until smooth. Evenly divide the cookie dough between two bowls and mix one with red food coloring and one with green.
Fold 1/2 cup white chocolate chips into each cookie dough. Take a small amount of each cookie dough and roll together into balls. Place onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.