Preheat oven to 350 degrees F (175 degrees C). Heavly grease two 9x5 inch loaf pans or bundt pan. In a microwave-safe bowl, microwave chocolate until melted. Stir occasionally until chocolate is smooth. Be careful not to overcook or it will taste burnt.
In a large bowl, combine eggs, sugar, oil, applesauce, grated zucchini, vanilla and chocolate; beat well. Stir in the flour, baking soda, salt and cinnamon. Fold in the chocolate chips. Pour batter into prepared pans.
Bake in preheated oven for 60 to 70 minutes, or until a toothpick inserted into the center of a loaf comes out clean.