Or similar ephemeral souvenir. Perhaps the Cast even has an autograph book they must keep track of, which they fill as they go.
Pros:
History is full of famous people, and signing autographs for fans is a recent thing.
Cons:
Less effective as you approach the present, and not really viable too far into the future, unless you want to get super-mean and require DNA samples or the like.
Fate Value: 3-6
Example:
"You will get Alexander the Great's autograph."