Mix confectioners' sugar, peanut butter, margarine, brown sugar, and vanilla together in a bowl. Press peanut butter mixture into the prepared pan.
Melt chocolate chips in the top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching.
Pour melted chocolate evenly over the peanut butter layer. Let buckeye bars cool completely before cutting into squares.
