Preheat oven to 250 degrees F (120 degrees C). Line 2 baking sheets with aluminum foil or parchment paper, and set aside.
In large metal or glass bowl, beat the egg whites on high speed with an electric mixer until soft peaks form. Gradually add sugar while continuing to beat until they hold stiff peaks. Mix in the vanilla and cocoa on low speed, then fold in chocolate chips by hand. Drop small mounds of the mixture onto the prepared baking sheets, spacing 1 inch apart.
Bake for 1 hour in the preheated oven. Turn off oven, and leave the cookies in the oven for 2 more hours, or until centers are dry. Remove from pan and store in an airtight container.