Grease a 9-inch square pan.

Melt butter in a large saucepan over medium heat. Stir in brown sugar and vanilla; mix in oats. Cook over low heat until ingredients are well blended, about 2 to 3 minutes. Press 1/2 of the mixture into the bottom of the prepared pan. Reserve remaining oat mixture for topping.

Meanwhile, melt chocolate chips and peanut butter in a small heavy saucepan over low heat, stirring frequently until smooth. Pour chocolate mixture over crust in the pan and spread evenly with a knife or the back of a spoon.

Crumble remaining oat mixture over chocolate layer, pressing down gently. Cover and refrigerate for 2 to 3 hours or overnight. Bring to room temperature before cutting into bars.