Line an 8-inch square baking dish (no larger) with parchment paper and set aside.
Melt butter and brown sugar in large saucepan over medium heat, until the butter has melted and the sugar has dissolved. Stir in vanilla. Mix in 3 cups of oats, reserving 1 tablespoon for topping.
Cook over low heat 3 to 4 minutes, or until ingredients are well blended.
Pour half of the oat mixture into the prepared baking dish. Spread out the mixture evenly, pressing down. Reserve the other half for second layer.
To make the filling, melt the peanut butter and chocolate chips together in a small microwave-safe bowl for 60 seconds on high; stir well and continue microwaving 10 seconds at a time until smooth.
Pour half the chocolate mixture over the oats, spreading it evenly over the top. Top with the second half of the oats and gently press until a single layer. Top with remaining chocolate mixture and sprinkle with the reserved oats.
Refrigerate 2 to 3 hours or overnight. Lift bars out the pan using the edges of the parchment paper and cut into squares.