Combine chocolate chips, condensed milk, butter, and milk in a small saucepan. Heat over low heat, stirring gently, until the sauce is smooth. Remove from heat and stir in vanilla extract.
Serve warm. Store hot fudge sauce in the refrigerator. Reheat sauce in the microwave or place a few inches of water into a pan and heat the water until warm but not boiling. Remove from the heat and place the jar of hot fudge in the pan for a few minutes.