Line a 9 x 9 inch pan with aluminum foil and grease with butter. Set aside.
In a large sauce pan, add the condensed milk, chocolate chips, and butter. Cook over low heat, stirring often to avoid burning. Cook until mixture is melted and well combined.
Remove from heat and add vanilla; stir until combined. Add in the marshmallows and fold into the fudge. Try to coat all the marshmallows with the fudge.
Pour mixture into the prepared pan. Spread evenly and then tap few times to remove air bubbles.
Place in the refrigerator to set for at least 2 hours.
When set, remove from pan using the foil and cut into pieces.
Store fudge in fridge for long storage. Just remove from fridge about 30 minutes or so before serving to soften.