Preheat the oven to 350 degrees F (175 degrees C). Grease an 8-inch square baking pan.
Combine flour, cocoa powder, baking soda, and salt in a bowl; set aside.
Place tofu in a blender; cover. Blend until smooth. Add sugar and olive oil; blend for 1 minute. Pour into a bowl; stir in vanilla extract.
Place bittersweet chocolate squares in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching until chocolate is melted. Stir melted chocolate into tofu mixture until combined. Stir in flour mixture until thoroughly combined, about 3 minutes. Fold in chocolate chips; transfer to the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool before slicing into bars.