1. Preheat oven to 350°F (180°C). Grease a 9 x 13-inch (3.5 L) baking dish; set aside.
2. Beat butter with peanut butter in a large bowl. Add granulated sugar and brown sugar; beat well. Add eggs, one at a time, beating well after each addition. Blend in the vanilla.
3. Stir flour with the baking powder and salt. Add the flour mixture to the peanut butter mixture; blend well. Stir in the peanut butter chips. Spread half of the batter into the prepared pan; spoon syrup over top. Carefully top with remaining batter. Swirl with a metal spatula or a knife for a marble effect.
4. Bake for 35 to 40 minutes or until lightly browned. Cool dish completely on a rack. Cut into squares.
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