The U.S. Senate's newest member had just popped into a local restaurant for a quick lunch when a waitress peered down at him and asked, "You are who I think you are, aren't you?" The object of her curiosity scrunched down in his booth, smiled sheepishly and whispered, "I'm Linc Chafee."

There was no back-slapping, handshaking or schmoozing as Chafee came and went, only a little banter with the waitress about how his father, the late Sen. John H. Chafee (R-R.I.), used to turn up at fund-raising events with white hairs from the family cat all over his dark suit.

Lincoln Davenport Chafee came to the Senate by virtue of one of the traditional passports to power in American politics: pedigree. When his father decided this spring to retire at the end of his fourth term, Chafee decided to run for the seat. And when his father died of heart failure in late October, the 46-year-old son was appointed by Rhode Island's Republican governor to fill out the last year of the term.

But there is little else about the younger Chafee that fits the stereotype of a U.S. senator.

A better listener than speaker, he is unpretentious, gentle in manner and language, candid to a fault, awkward at times and perhaps, as an article in the December issue of the Rhode Island Monthly put it, a little "quirky." And his resume is unique for the Senate: A classics graduate from Brown University who was born to wealth and privilege, he spent seven years shoeing horses at harness race tracks in the West before returning home for a career in business and politics.

Friends caution against underestimating him, however, pointing to his successful record as mayor of Warwick, Rhode Island's second-largest city, and to the favorable response he has received since his appointment to the Senate.

A moderate Republican in his father's mold, Chafee broke a 32-year Democratic reign in Warwick, population roughly 86,000, when he was elected mayor in 1992. He made his mark early by settling a bitter teachers strike that contributed to his defeat of the incumbent mayor. He was reelected three times, and, in his last race, he won all nine wards and had the backing of most municipal unions. "He was a very successful mayor," said Darrell West, a political science professor at Brown.

Although Democrats were initially favored to pick up the seat, it is now "viewed as . . . his to lose," said Rep. Patrick J. Kennedy (D-R.I.). Rhode Island is one of the most Democratic states in the country, but Republicans can win when Democrats fight each other. This is what happened when the senior Chafee first won his Senate seat in 1976, and Democrats concede it could happen again next year in what many here expect to be a fierce struggle for the Democratic nomination to oppose the younger Chafee.

Chafee's handling of questions about drug use that arose after Texas Gov. George W. Bush dodged the issue this summer demonstrated how his unorthodox approach to politics--especially his candor--pays off, either intentionally or coincidentally.

Once Bush made headlines by refusing to say whether he used cocaine in his youth, Chafee knew he would be asked the same question. And he knew what the answer had to be: He had tried cocaine several times in the early 1970s. He would not lie, he said, and "I tried to think of every way out, but there was none. . . . I simply had no choice" but to admit it, which he did in a television interview the next day. He shot up 10 points in the next poll, and pundits credited him with a successful exercise in political inoculation. Not so, says Chafee. "There was simply nothing else I could do," he says.

Chafee's biggest challenge will be filling the shoes of his father, who, as governor, secretary of the Navy and four-term senator, was revered as a man of courage and decency, in Rhode Island and the Senate. Their politics are virtually the same, although the son appears more liberal than the father on some issues, such as labor unions.

The question is whether Lincoln Chafee will be as tough as John Chafee was in standing up to conservative pressures from his own party or as tenacious as his father in trying to bridge partisan differences on such issues as health, education and the environment.

Some have their doubts, but Gov. Lincoln Almond (R), who appointed the younger Chafee, said, "He's a lot like his dad; he'll vote what he thinks is right."

"Linc wasn't a Marine, he doesn't have a take-charge way about him," said Jonathan Stevens, a childhood friend who worked with Chafee in Warwick and is with him in Washington. He may lack assertiveness, "but that should never be mistaken for lack of resolve and commitment. . . . He's a thoughtful and deliberate decision-maker," Stevens said.

In an interview in his Providence office, Chafee seemed at ease with questions about how he will measure up.

"I can honestly say there is so much to admire in his viewpoint. . . . I aspire to be similar," he said of his father. He will try to "build bridges," as his father did, but believes he demonstrated in Warwick that he will also "stand up for what I believe in" and has said as much to Senate Majority Leader Trent Lott (R-Miss.) and other conservatives. They indicated they understood, he said. "I credit my father for the inspiration to do this," he added.

In the three weeks he served in the Senate before its pre-Thanksgiving adjournment, Chafee faced only one big test of the kind that often separated his father from most other Republicans: a proposed $1 increase in the minimum wage. He joined with three of his father's allies--Sens. Arlen Specter (Pa.), Olympia J. Snowe (Maine) and James M. Jeffords (Vt.)--in voting for both the Democrats' bill as well as a less expansive version advanced by GOP leaders, bringing the Democrats within two votes of prevailing.

He sees his differences with his father over organized labor as mainly generational. While John Chafee saw unions' rise to political power in Rhode Island as a threat to industry and jobs, his son said he learned to work harmoniously with unions in city government and has come to recognize their "permanence and value."

One of six children in a close-knit family with patrician roots, Chafee grew up while his father was in public office. He came by his individualism naturally. "My mother was an organic gardener back before most people knew the term," he recalled. "We ate brown bread, much to our embarrassment when everyone else had Wonder Bread in their lunch boxes at school. We even had long hair before the Beatles came around." Along the way, he also acquired a love of horses and, through summer jobs, a taste for hard labor.

Chafee attended public schools but finished up at a prestigious private boarding school and then Brown. When he graduated in 1975, he wanted to "try something different before embarking on a high-pressure career," which turned out to be a 12-week course in horse-shoeing at Montana State University and seven years on the harness-racing circuit in the United States and Canada.

It was what many young people did in the '70s, he said. "It was a good life, learning a trade, working hard," he said. "It was far from 'dropping out.' It was just a different path."

Eventually, Chafee returned to Rhode Island, where he took a succession of corporate jobs before striking out on his own again--this time into politics, first as a successful candidate for a state constitutional convention, then winning election to the Warwick city council. He lost the first time he ran for mayor but won the second time.

Competing for the Democratic nomination to oppose Chafee next year are Rep. Robert A. Weygand and lawyer Richard Licht, with Arlene Violet, a radio talk show host, ex-nun and former state attorney general, talking about running as an independent.

Weygand and Licht are both 51, former lieutenant governors and friends who agree on most issues. But both are also intense, hard-charging and worried already that a bloody campaign for a primary that occurs only two months before the November election could be disastrous for the victor. "That," says Weygand, "could be one of the biggest advantages for Lincoln Chafee."