Place the marshmallows in a large, microwave-safe bowl, reserving about one cup of marshmallows for later use.
Add the butter to the bowl with the marshmallows and heat on high for 1 minute. Stir well, then continue heating in 30-second intervals, stirring between each, until the butter has fully melted.
Stir in the vanilla extract until the mixture is smooth, allowing it to cool slightly.
Add the reserved marshmallows and then stir in the crispy rice cereal, mixing thoroughly with a wooden spoon or rubber spatula until the cereal is evenly coated.
Gently fold in the mini chocolate chips, working quickly to prevent them from melting.
Transfer the mixture to a buttered 9x9 pan, using a buttered spatula (or a piece of plastic wrap) to press the mixture firmly into the pan.
Let the treats cool completely before slicing into bars.