Nobody's complaining of unfair advantage being taken. New York Democrats need someone to keep a Senate seat out of the clutches of Mayor Rudy Giuliani, and Hillary Clinton is looking for a lifetime career opportunity. Their needs dovetail. The only impediment to the match, the wanly hopeful Rep. Nita M. Lowey (D-N.Y.), went quietly.

Plans proceed amid high excitement and heady talk--the rumor is that former Treasury secretary Robert Rubin and erstwhile White House chief of staff Erskine Bowles will head the fund-raising. The jest, a jocose suggestion last October from Rep. Charlie Rangel of Manhattan, has become a quest.

It is becoming the most riveting race in the country, promising endless novelty and surprise. When has a first lady ever run for office? Will there be conjugal visits? Will the First Couple walk down Fifth Avenue on Sunday mornings hand in hand, clutching their Bibles?

Indications are that New York Democrats are amenable to precedent shattering. They will certainly be shattering precedents if they are accomplices in creating a part-time first lady. They know, as who does not, the perils of leaving the First Citizen home alone. They know how ill-suited the president is to solitude--he told dinner guests he would be "a basket case" if he were on his own in the vast, haunted executive mansion. He remembered the misery of Harry Truman when Bess decamped every summer for Independence, Mo.

It is apparently okay if Hillary gets out of town, and wants to get even by showing her stuff after a lifetime spent in the shadow of a politician who was thought to be the most dazzling and the luckiest public figure of his generation. Voters approve of Hillary's independence, they understand that her celebrity is derivative. Her feminism is fine with them.

And now comes the paradox, the central riddle of her relationship with the people of New York. She can travel the globe, lecture the Chinese and the Brazilians, rally Africans; she can challenge the people of Oneonta, Queens and Westchester County. But, polls suggest, she must not leave Bill. It is permissible to exploit his name and job by running for the Senate in New York. She must swallow the shame and humiliation of Monica and all the others, but she must preserve the marriage. For a nation with a 50-percent divorce rate, this is bizarre, to say the least. Will it hold, if she progresses in an orderly way up the ladder? If she is eventually elected president, will her husband accompany her to the White House?

The one thing that caused her approval rating to dip at all was the rumor that she was about to leave her husband. It was in the spring, when the president went to Central America on his own. When the moment passed, her rating crept back up again. John Zogby, the upstate pollster, says there are two questions voters would like to have answered. One is "Why do you want to be senator from New York?" The other is "Why did you stay with him?"

The New York tabloids can be trusted to see that these matters are explored.

Will the president be able to keep out of his wife's New York business? Probably not. He suffers from candidate envy, as he revealed in an interview with the New York Times, when he meanly shared his reservations about his putative successor's progress. Also Bob Dole, a past presidential contender, did not set an example of the ideal candidate's husband. He mused that he might write a check to his wife's rival, John McCain.

Giuliani is strong, but vulnerable. He will contest every inch of turf, as New Yorkers always do. But the appalling case of Abner Louima, who was tortured while in the custody of the NYPD, has caused widespread alienation among minorities. And then there is the subject of what is called "Clinton fatigue"--an aversion to sex, lies and videotape, to scandal, coverup and a hard-to-explain marriage. Giuliani is the last person in the world to exploit this factor: He and his wife, Donna Hanover, have not explained the state of their union to anybody's satisfaction but their own.

The conventional wisdom is that Hillary 's enveloping celebrity will fall short in upstate New York, where Giuliani's disdain for carpetbaggers is most widely reflected and where uppity women from Wellesley are not welcome. Mrs. Clinton is sometimes thought to be more liberal than her husband, although that is not necessarily so. That part of her reputation derives much from her ill-fated health plan, a top-heavy, unworkable affair that shows what can happen when a person of her overwhelming self-confidence and intellectual pretensions gets her head.

The Senate race gives her a chance to get out of Washington and move on. If she makes it, there's no end to her horizons, and the country may have to fasten its seat belt for another round of Clinton politics. New York appears to be ready--if Hillary stands by her man.