Generally speaking, you can keep the chuck roast in the refrigerator for about three to five days after purchasing it from the store. The meat will last the longest if you keep it in your original packaging. Uncooked chuck roast can also be stored in the freezer for future use. Take the meat in its original packaging and wrap it with aluminum foil. Put the wrapped meat inside a larger freezer bag. You can expect your chuck roast to retain its original quality for about six to 12 months. Cooked chuck roast is typically good for about three to five days in the refrigerator and about three months in the freezer.