Preheat the oven to 350°F (175°C). Grease and flour a 9×9 inch square baking 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, then mix in the vanilla extract.
Stir in the mashed ripe bananas and sour cream until combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Fold in the semisweet chocolate chips evenly throughout the batter.
Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and allow the cake to cool in the pan on a wire rack for 15 minutes.
After cooling, remove the cake from the pan and let it cool completely on the wire rack before slicing and serving.