Grease a 9x13-inch baking pan or line it with parchment paper. Measure the Chex cereal into a large mixing bowl and set aside.
In a medium saucepan, combine the light corn syrup and granulated sugar. Bring the mixture to a gentle boil over medium heat, stirring frequently until the sugar dissolves.
Remove from heat immediately. Stir in the creamy peanut butter until the mixture is uniform and silky smooth.
Pour the hot peanut butter syrup over the Chex cereal in the bowl. Using a large silicone spatula, gently fold the cereal until every piece is evenly coated without crushing the Chex grids.
Transfer the coated cereal to the prepared 9x13-inch pan. Lightly press the mixture into an even layer using the back of a buttered spatula.
In a microwave-safe bowl, combine the chocolate chips and butterscotch chips. Microwave in 30-second intervals at 50% power, stirring between intervals, until completely melted.
Spread the melted chocolate-butterscotch topping evenly over the Chex layer.
Allow the bars to set at room temperature for 45 minutes or chill in the refrigerator for 20 minutes before cutting into 24 bars.