In a microwave safe bowl, add peanut butter, non-dairy butter, and dairy-free chocolate chips.
Microwave in 30-second increments, mixing in between, until the chocolate is melted. It should take just about 1 minute total.
Add the Rice Chex cereal to a large bowl. Pour the chocolate peanut butter mixture over the cereal. With a spatula, carefully mix until the cereal is completely covered with the chocolate.
Add the chocolate covered cereal to a large tupperware with a lid or a gallon-sized Ziploc bag. Add 2 1/2 cups of the powdered sugar. Shake the container until the powdered sugar has covered the cereal. If the cereal is not completely covered or you can see chocolate showing through the powdered sugar, add the remaining 1/2 cup of powdered sugar.
You can serve right away or store at room temperature. However, I prefer to store in the refrigerator and chill for at least an hour for cold puppy chow.