The Shinnecock Indians have a grand idea.

They want this wealthiest of Long Island beach towns to give back to the tribe about 3,600 acres, encompassing the posh Shinnecock Hills Golf Club and a few multimillion-dollar waterfront chateaus. Southampton's forefathers long ago obtained this land -- valued at a tidy $1.7 billion today -- from the Shinnecocks under questionable circumstances.

Or, alternatively, Southampton's town leaders could keep their land and allow the Shinnecocks to construct a $20 million casino on sandy bluffs overlooking Peconic Bay.

"We've complained until we are blue in the face -- now we seek justice," said Randy King, the taciturn chairman of the tribe's board of trustees, which earlier this month filed a land-claims lawsuit against Southampton in U.S. District Court. "Think of it as a civics lesson. Think of it as 'Put up or shut up.' "

Several wealthy investors, including Detroit businessman Michael Ilitch -- who owns the Detroit Tigers baseball team -- are financing the tribe's legal battles, in hopes of persuading the town to yield on a casino.

None of this amuses the non-Indian natives. Many Southampton officials view the land claims as preposterous and the proposed casino as a disaster, threatening to bring gambling fever and more cars to the gridlocked reaches of eastern Long Island. They have rallied political support -- both of the state's U.S. senators, Charles E. Schumer and Hillary Rodham Clinton, oppose a casino -- and have hired a lawyer to fight the land claims in court.

Southampton Supervisor Patrick A. Heaney has stopped talking to the media about the matter. But early on he told a Newsday reporter: "I don't think it's my obligation, personally, to carry some great angst about the relationship between townspeople historically and people living on the reservation."

As for the moneyed Manhattanites who are thick on Southampton's oak-shaded streets this time of year? The summer season has shifted into high gear, as private helicopters ferry the plutocratic set -- such as financier Henry Kravis and former ambassador to France Felix G. Rohatyn -- to weekend mansions and $1,000-a-plate dinner parties (the Animal Rescue Fund's Ciao Ciao Bow Wow soiree is all the buzz just now).

But few of these worthies are sweating the question of land claims.

"This dispute isn't on their tongues -- in fact, I haven't heard a word," said Joan Jedell, publisher of the Hampton Sheet, which chronicles every champagned step of the rich and deeply tanned. "The high-net-worth crowd doesn't really worry about this sort of thing. That's for the locals."

Over at the Shinnecock Hills Golf Club, which has harbored generations of Rockefellers, du Ponts and Vanderbilts, mum's the word.

"We have no comment at all," General Manager Greg Dreger said. "Really, just no comment."

The Shinnecocks, known as the People of the Shore, have watched their tribal lands dwindle over the years. In the halcyon days before European colonists set foot in the New World, the Shinnecocks and Montauketts, both Algonquin tribes, controlled a long stretch of sandy beaches and marshes and highland bluffs. In 1640, English settlers arrived and bought about eight square miles of land from the Shinnecocks, for the not-so-princely sum of $20.

There were many subsequent land takings by the colonists, culminating in the almost certainly fraudulent Great Dispossession of 1859, when a group of private investors sought to finance a line of the Long Island Rail Road east to Montauk Point. These investors persuaded 20 or so Shinnecocks to sign a petition deeding the land to the investors.

Other tribal members traveled to the state Capitol in Albany to protest the land grab, but to no avail. The Shinnecock Nation lost thousands of acres. The tribe was left with an 800-acre state-recognized reservation, a verdant swath of grassy fields, forest and vines sweeping to the eastern beaches of Shinnecock Bay. That bay empties into the Atlantic Ocean.

"Growing up here, you were always aware of the loss," said Beverly Jensen, a tribal spokeswoman. "The elders would point it out and say, 'This was your land.' "

Six hundred Shinnecocks live on this land, which has a feeling out of time to it. Save by invitation, none but Shinnecocks are allowed. Children of 12 or 13 drive automobiles and motorbikes on the reservation, and horses range across the fields. Many of the Shinnecocks are quite poor, but there are doctors and lawyers as well.

The tribe has held annual elections for the tribal council since 1792, and the results are recorded at Southampton Town Hall. But the Shinnecocks have only recently applied for tribal recognition by the federal Bureau of Indian Affairs, which would in turn allow them to open a casino. To obtain federal recognition, the Shinnecocks must establish the genealogy of every Indian living on the reservation.

That is no easy matter, not least because some family records are lost in time's mists and because many Shinnecocks long ago intermarried with the black slaves and white indentured servants who labored beside them in the potato fields and cornfields of white owners. What is left is a very American identity spin -- many, although by no means all, of the Shinnecocks appear more African American than stereotypically Indian.

"There's this sense of racial hierarchy in America," said historian John A. Strong, whose book "We Are Still Here" tells the story of the Algonquin tribes of Long Island. "White are on top, Indians are in the middle, and blacks are at the bottom.

"If an Indian marries a black, white people are likely to insist, 'Oh, your child is black, not Indian.' "

Michael Smith, 56, is pastor of the Presbyterian Church on the reservation, a tribal member of centuries-old pedigree, and a lean man with African American features. He spreads his arms.

"We are unique," he said, "in that we inhabit the lands of our ancestors and we recognize the fullness and richness of our humanity."

Smith is one of several Shinnecocks who view the tribe's land-claims lawsuit against Southampton as ill-advised. It has inflamed local sentiment, he said, and guaranteed the tribe will face a tough fight for federal recognition. And he is suspicious of the motives of millionaire investors who are underwriting the lawsuits.

"Folks on the reservation have this notion that there's going to be a great influx of money when the casino is built, and that's not real," Smith said.

King, the tribal chairman, gets a little testy talking about the casino and land claims. As he sees it, his tribe should not have to explain anything. But he allows that the tribe has no ambition to construct a beachside version of Foxwoods, the mammoth casino in Connecticut. The Shinnecocks' casino, he says, would be about the size of a supermarket.

"You want to talk traffic? It's all the crazy development that brings traffic," he said. "We have to care for our elderly and pay our bills. What folks have to understand is that this is our land."

"We seek justice," said Randy King, center, chairman of the Shinnecock Indian tribe's board of trustees, who with fellow trustees filed a land-claims lawsuit earlier this month. Rockefellers and Vanderbilts have been members of the exclusive Shinnecock Hills Golf Club, located on the 3,600 acres of prime Long Island land that the Shinnecocks are seeking.