Line a cookie sheet with waxed paper; set it aside. Using a wooden spoon, mix together the peanut butter, sugar, butter, vanilla extract, and graham crackers, if desired, in a large bowl. (The dough will look dry.)
Roll the dough into 1-inch balls. Set them on the prepared cookie sheet and insert a toothpick into each ball. Chill them in the freezer until hard, about 30 minutes.
Melt the chocolate chips in a heatproof bowl set atop a pot of simmering water over medium-high heat. Stir continuously until smooth. Remove the pan from the heat. Using the toothpick as a handle, dip the balls into the melted chocolate, leaving a small circle at the top uncovered. Place the dipped candies back on the cookie sheet and refrigerate until the chocolate is set, about 2 hours. Store in an airtight container in the refrigerator.