Grease an 8-inch square pan and line the bottom with parchment paper. Set aside.
In a small saucepan, heat 2 cups of the marshmallows and butter over low heat, stirring occasionally, until completely melted. Pour the marshmallow mixture over the shredded wheat in a large bowl and stir until evenly coated. Stir in remaining marshmallows and ½ cup of chocolate chips.
Press the mixture firmly into the bottom of the prepared pan and let cool for at least an hour or until firm. Invert the bars out onto a cutting board and slice them into squares or rectangles.
Place the remaining chocolate chips and oil in a microwave-safe bowl. Microwave according to the package directions until fully melted and smooth. Drizzle over the bars. Store the bars at room temperature for up to 1 week.