Line a large rimmed baking sheet with parchment or wax paper. Set aside.
In a large mixing bowl, beat together the crushed crackers, peanut butter, butter, powdered sugar and vanilla. Blend on medium until combined. The mixture may appear dry, but keep beating until it forms a soft, but cohesive, dough.
Using a small cookie scoop, roll dough into 1 1/4-inch balls and place on the prepared baking sheet. Freeze until the dough balls are firm, about 1 hour.
Microwave 1 cup of the semisweet chocolate chips in a bowl on 50% power, stirring halfway through, until melted, about 1 ½ to 2 minutes.
Using a toothpick, dip chilled balls into the melted chocolate, leaving the top third of the balls uncovered. Return the Buckeyes to the lined baking sheet and refrigerate until the chocolate is set, about 1 hour.