Preheat your oven to 350° F. Grease a 9 x 5 inch loaf pan or line with parchment paper.
In a microwave-safe bowl, melt your semi-sweet chocolate chips in the microwave by heating for about a minute. Stir until smooth. Set aside to cool slightly.
Next, prepare the banana bread batter. In a medium mixing bowl, add the sugar, vegetable oil, and eggs. Whisk until completely smooth and light yellow in color. Add the mashed bananas and vanilla. Mix well.
In separate bowl, stir together the flour, baking soda, and salt. Pour these dry ingredients into the banana mixture, and stir with a spatula just until the flour is incorporated.
Add 1 cup of the banana bread batter to the cooled melted chocolate and stir immediately to prevent the chocolate from hardening. Also add the 1 teaspoon cocoa powder and mix until smooth. The chocolate batter will be fairly thick.
Pour a layer of the plain batter into your greased loaf pan. Then add some of the chocolate batter. Repeat with the remaining batter. Using a butter knife, swirl the batter lengthwise and widthwise about five times each direction. Do not over-swirl because you want a marbled effect so the batters should not completely blend.
Bake for approximately 50-60 minutes, or until a tester comes out clean in the center of the bread. Let cool slightly before removing from the pan.