Preheat the oven to 350°F (175°C). Grease and flour a 9×9 inch (23×23 cm) square cake pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy using an electric mixer.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract.
Add the mashed bananas to the wet mixture and stir to combine.
Alternately add the dry ingredients and the buttermilk to the wet ingredients, beginning and ending with the dry ingredients. Mix just until combined; do not overmix.
Fold in the semi-sweet chocolate chips evenly into the batter.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before slicing and serving.