Line one large baking sheet with aluminum foil and another with waxed paper; set both aside. Beat together the peanut butter and butter in a large bowl until blended and smooth. Add the sugar, 1/2 cup at a time; blend until smooth. Press the mixture into 1-inch balls. Place the balls on the foil-lined sheet. Let stand until firm, for about 30 minutes. Melt the chocolate chips and shortening in a heatproof bowl, setting atop a pot of simmering water over medium-high heat. Stir continuously until smooth. Remove the pan from the heat. Using a toothpick for a handle pierce each ball, then dip into the melted chocolate. Spoon chocolate over the balls to coat them, if needed. Set the balls on the waxed-paper-lined sheet and top each with a peanut half. Refrigerate until set for about 30 minutes.
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