Divide Chex cereal into two large bowls (3 cups in each bowl).
Crush Oreos into fine crumbs using a food processor or by putting them in a Ziploc bag and crushing them with a rolling pin. Divide the Oreo crumbs evenly into two separate Ziploc bags (about ½ cup in each bag). Add ½ cup of powdered sugar to each bag. Set aside.
Melt the milk chocolate chips– I like to use a double boiler, but you can also melt them in the microwave, stirring every 30 seconds until melted. Pour the melted chocolate into one of the bowls of Chex cereal and stir gently until the cereal is evenly coated in chocolate.
Melt the white chocolate chips. Pour the melted white chocolate into the other bowl with Chex cereal and stir gently until the cereal is evenly coated in white chocolate.
Add the milk chocolate Chex to one of the gallon Ziploc bags, and the add the white chocolate Chex to the other gallon Ziploc bag and shake the bags well to evenly coat the cereal with powdered sugar.
Pour both bags together into one large bowl. And if you've got any extra Oreos in your package, chop some up and add them to the mix!