Preheat the oven to 325 degrees F (165 degrees C). Grease a 9x13 inch baking pan.
In a large bowl, cream together the butter, white sugar and brown sugar until smooth. Beat in the egg, 1/3 cup peanut butter and vanilla.
Combine the flour, baking soda and salt; stir into the peanut butter mixture. Finally, mix in the rolled oats. Spread the dough evenly into the prepared pan.
Bake for 20 to 25 minutes in the preheated oven, or until edges are firm. Remove from the oven and sprinkle the chocolate chips in a single layer over the top. Let stand for 5 minutes, then spread to cover. Allow to cool.
In a small bowl, mix together the confectioners' sugar, 1/4 cup peanut butter until smooth. Stir in milk one tablespoon at a time until a drizzling consistency is reached. Drizzle over bars when cool. Cut into bars.