Prepare an 8½ × 11-inch pan by lightly oiling it or lining it with parchment paper; measure all ingredients before starting.
In a medium pot over medium heat, melt the butter until fully liquid.
Stir the peanut butter into the melted butter until smooth, about 1 minute.
Add the mini marshmallows to the pot and cook over medium-low heat, stirring constantly, until they soften, stretch, and begin to lose their shape, about 1–2 minutes; then remove the pot from the heat.
Immediately add the Rice Krispies cereal to the marshmallow mixture and stir until the cereal is evenly coated.
Pour the mixture into the prepared pan and spread it evenly with a spatula; wet your fingers and gently press the mixture into the pan to compact it slightly without pressing too hard.
Combine the chocolate chips and coconut oil in a microwave-safe bowl and microwave at half power, stirring every 30 seconds, until melted and smooth (about 1–2 minutes total).
Pour the melted chocolate mixture over the pressed cereal layer and spread into an even layer with a spatula.
Let the bars cool completely at room temperature until the chocolate is set, then slice into 12 bars and serve.