PHILADELPHIA — Who owns 10 exceedingly rare American gold coins from 1933?

Is it the family of a local gold dealer who died 21 years ago? Or is it the United States government, which produced a half million of the coins before melting all of them — well, almost all of them — down?

Family members, who say they found the coins in a safe deposit box in 2003, argue they are the rightful owners of the exquisite “double eagle” $20 coins, each now worth millions of dollars. The government argues that the coins, never officially released, belong to the United States, and not the heirs of Israel Switt, the gold dealer.

And so to court.

In a case that began on Thursday, jurors are getting an unusual lesson in Depression-era history, and will ultimately decide whether Mr. Switt was merely “colorful,” as a lawyer for the family described him, or a thief.