Justice Rehnquist, as he is addressed, had been formally summoned to the legislature in the first immutable sign that the 42nd President of the United States is now on trial.
According to legal experts, who have been keen to point up the differences between an impeachment trial in the Senate and a trial in court, Justice Rehnquist will be more arbiter than facilitator. While the senators will be sworn in effectively as jurors and must be mute throughout proceedings, they are not consigned to the role of trial jurors, listening and watching passively until called upon for their verdict.
They have the power to halt or annul proceedings, at almost any moment, by sending a written request for a vote. If by a simple majority, 51 votes, they decide they do not approve of the way the trial is going, or the way the Chief Justice is presiding, they can call off the whole enterprise. But, of course, they must weigh that against their constitutional duty to try the President, a duty imposed upon them as soon as the House of Representatives passed articles of impeachment last month.
Mr Clinton may be on trial but so is the Chief Justice and so is the Senate. According to The Washington Post's judicial correspondent, the Chief Justice's function will be to moderate proceedings: to keep order in the chamber, rule on matters of evidence and determine the pace of proceedings.
He will also be a kind of "postman", receiving written questions from the senators and passing them on to the witnesses.
The last word is his only if the trial goes to a final "jury" vote and that is tied. Then the fate of the President rests in his hands; only at that point is the authority of the judiciary above that of the legislature and the chief executive.
Since the prospect of a Senate trial was first broached in autumn, Justice Rehnquist has been the centre of the sort of attention that he has consistently - and successfully - eschewed for much of his career. Described as a "very private person", he is admired by the lawyers who have dealings with him as a consummate professional, with a fine sense of the law, but also the authority and managerial ability that allows the Supreme Court to run as though on wheels.
As a judge, and for the past 12 years as the head of the Supreme Court, Justice Rehnquist has a reputation for scrupulous fairness and a quiet, short temper: he is said to be intolerant of the slightest rustle of paper or conversation in his courtroom, and establishes silence before proceedings can resume. Spotted in the vicinity of the Capitol and the Supreme Court the day before he was due to be summoned to the Senate, Justice Rehnquist was taking an early- morning walk, wearing a blue anorak, carrying newspapers under his arm. To anyone who did not know him by sight - which is most Americans - he was indistinguishable from any of the other early-morning walkers.
Hailed by television reporters, he simply gave a polite smile and "Hello", and a glancing question about what had brought them out so early, and went on his way.
As his name suggests, Justice Rehnquist is of Swedish origin and, while he does not speak the language, he preserves Scandinavian ties, attending - or encouraging members of his family to attend - Swedish events in Washington and showing a fondness for his Nordic roots.
Politically, he is a conservative and was a Republican appointee to the Supreme Court, but even the most outspoken Democrats have expressed no qualms about his ability to be impartial in the trial to come.
To some, there is a mismatch between the hallowed and dignified atmosphere of the Supreme Court, which is seen as Justice Rehnquist's natural habitat, and the gossipy, adversarial atmosphere of the Capitol. Aficionados note, though, that the Senate is a quite different place from the House of Representatives; quieter, more dignified and more conscious, self-conscious perhaps, of its own importance. More than half the members of the new Senate - 52 - are lawyers by training.
It is pure coincidence, but a fortunate one, that one of William Rehnquist's personal interests as a lawyer is the area of impeachment. In 1992, when he published a book on historic impeachment cases, including that of Andrew Johnson, the last and up to now only president to be impeached, he can hardly have dreamt that it would fall to him to preside at the only presidential impeachment trial this century. That is his honour, and his burden.