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