Preheat oven to 350 degrees. Lightly grease and flour a 9x5-inch loaf pan and set aside.
In a medium bowl, mix together the flour, cocoa powder, baking powder and salt.
In a separate bowl, use an electric mixer to beat together the yogurt, honey, egg and vanilla.
Add half the flour mixture into the yogurt mixture and beat on low speed while slowly pouring in half the milk. Turn mixer off, scrape down the sides with a spatula and then add remaining flour mixture to the bowl with the remaining milk.
Stir in the mashed bananas until well combined. Fold in the chocolate chips.
Spread batter into prepared loaf pan. Press more chocolate chips into the top of the batter before baking, if desired.
Bake on the middle rack of the oven for about 50 minutes or until a toothpick inserted in the center of the loaf comes out clean.
Let the bread cool in the pan for about 20 minutes before removing to a wire rack to cool completely.