Measure the Chex cereal into a large mixing bowl and set aside. Make sure the bowl is big enough for tossing everything later.
In a microwave-safe bowl, combine the chocolate chips, peanut butter, and butter. Microwave in 30-second intervals, stirring after each, until the mixture is melted and smooth (about 1½ to 2 minutes total). Stir in the vanilla extract once melted.
Pour the chocolate mixture over the cereal. Gently fold with a spatula until every piece is evenly coated. Be careful not to crush the cereal.
Place the coated cereal in a large zip-top bag (or use a clean, large container with a lid). Add the powdered sugar and crushed Butterfinger. Seal the bag and shake vigorously until all pieces are fully coated.
Spread the finished puppy chow on a parchment-lined baking sheet to cool and set for about 10 minutes. Once dry, transfer to a serving bowl or airtight container.