Yes, you can make chocolate buttercream frosting ahead of time and store it. In fact, making frosting in advance can be a great time-saver, especially if you're planning to decorate a cake or cupcakes. To store chocolate buttercream frosting, transfer it to an airtight container and refrigerate it for up to 5 days. Before using the frosting, let it come to room temperature and give it a quick stir to bring it back to a smooth consistency. If you need to store the frosting for longer than 5 days, you can freeze it for up to 3 months. Place the frosting in an airtight container or a freezer-safe plastic bag and freeze it. To use the frosting, thaw it in the refrigerator overnight, and then let it come to room temperature and give it a quick stir to bring it back to a smooth consistency. It's important to note that the texture of the frosting may change slightly after being stored in the refrigerator or freezer. If the frosting becomes too stiff or difficult to spread, you can try adding a small amount of heavy cream or milk and beating it again until it becomes smooth and creamy.