For a chance to just look at the rarest modern American coin with his own eyes, David Hall will spend $10,000 — again.

Hall, president of Collectors Universe and co-founder of Professional Coin Grading Service, says the money is “absolutely” worth it to prove that at least one 1964-dated silver Peace dollar still exists.

According to U.S. Mint records, 316,076 Peace dollars were struck at the Denver Mint in May of 1965. But all were condemned to the melting pot in a tangled tale of political maneuvering and silver hoarding.

“Legend has it that there may be a survivor or two,” said Professional Coin Grading Service president Don Willis. ”

We’d love to determine if one still exists.”

Offering a reward to non-numismatists who may unknowingly have millions of dollars in rare coins sitting around at home has worked for Hall in the past.

In 2003, Collectors Universe issued a $10,000 reward for anyone in possession of a 1913-dated Liberty Head nickel. Only five were ever struck, and four were publicly accounted for.

The possibility of the missing coin turning up was painfully low.

But then the heirs of a 1940s coin collector saw an Associated Press story about the fabled coin’s value — a minimum $1 million — and dug it out of their mother’s house in Salem, Va.

Hall gave the family $10,000 for the privilege of authenticating the coin. He spent 40 minutes verifying it against the other four 1913-dated Liberty Head nickels in July 2003.

“It was amazing, they just had it sitting in the closet — had no clue,” Hall said. “Now I hear they’re going to sell it in April for $3 million to $4 million.”

The 1964-dated Peace dollar is different than most rare coins. It was modeled after the 1929-1935 Peace dollars circulated at the end of World War I. But the coins never saw the light of day.

On Jan. 11, Hall and the PCGS launched a “Top 100 Modern Coins” promotion and listed the 1964-dated silver Peace dollar as the most sought after coin minted after 1965.

The reason for the coin’s scarcity is simple: According the the U.S. government, it doesn’t exist.

In a 1998 article for Professional Coin Grading Service, COINage magazine senior editor Ed Reiter explained the complicated history of the 1964-dated Peace coin.

President Lyndon B. Johnson pushed to make the coins, despite protests from Congress. Johnson was roadblocked until May 15, 1965, when the he issued a presidential order to begin manufacturing the 1964 silver dollars — which is why the coins are backdated.

But a massive silver shortage made the coins more valuable for their silver content — 90 percent — than their $1 face value. Before they were to be released, private collectors advertising offers of $7.50 each spurred worries about hoarding of public currency, Reiter said.

“When word of the coins’ production got back to congressional opponents, they angrily demanded immediate suspension of the program,” Reiter wrote. “And Mint officials cheerfully complied.”

According the official story, all but two of the coins were destroyed.

The survivors were sent to Washington, D.C., where they remained until 1970, where Mint records say they too were melted in the presence of a destruction committee.

But Hall and other rare coin experts are not convinced.

“Credible rumors” from the underground numismatics culture give them hope.

“Supposedly every employee in the Denver Mint at the time received two coins each,” Hall said. “Or employees could have taken them without permission.”

Hall said a trusted Denver-based coin collector named Dan Brown claimed he saw one in the 1970s.

Today, it is illegal to possess a 1964-dated Peace dollar because they were not released to the public. Any examples of the coin found belong the U.S. government.

Hall said he’s willing to work with the terms of whomever actually has one of the coins in order to authenticate it. To claim the reward, he said a person must contact a PCGS chapter.

Because of its “non-existent” status, Hall said it’s impossible to say how much a 1964-dated Peace dollar would bring the holder, but guessed the price could top $1 million.

“If it exists, it would be one of the great coins of the 20th century,” Hall said. “There’s no doubt in my mind that we could identify it immediately.”

Megan Mitchell: 303-954-1223, mmitchell@denverpost.com or twitter.com/megs_report