Preheat oven to 350°F. Line a 9" x 5" loaf pan with parchment paper, and lightly grease.
In a medium-sized bowl, mash the banana with a fork. Stir in the plant-based milk, oil, vinegar and vanilla extract. Set aside.
In a large bowl, sift together the flour, sugar, cocoa powder, baking soda, and salt. Whisk until well blended. Add the wet ingredients to the flour mixture and mix just until the flour is almost blended. Add one cup of the chocolate chips. Stir until just incorporated. Do not over mix.
Pour the batter into the prepared pan and sprinkle with the remaining 1/4 cup of chocolate chips.
Bake for 55-65 minutes or until a toothpick comes out clean or with a few cooked crumbs stuck to it (keep in mind you may hit a melted chocolate chip so you may have to test a couple of spots.) Remove from the oven and let rest for 10 minutes before turning out of the pan onto a wire rack to cool.