THE ANNOUNCEMENT by special prosecutor Arthur H. Christy that a special federal grand jury voted unanimously not to bring any criminal charges against Hamilton Jordan, the White House chief of staff, is hardly a surprise. The charge that Mr. Jordan snorted cocaine in a New York disco in 1978 looked weak from the moment it was first made -- during plea bargaining by two big-time tax cheats. A second charge, that he used cocaine at a party in California in 1977, never contained enough substance to be taken seriously except by those who were eagerly seeking dirty on President Carter's closest adviser.

Nevertheless, it has taken a full FBI investigation, careful consideration by the attorney general, the appointment of a special prosecutor, 19 meetings of a special grand jury during which 33 witnesses gave sworn testimony, and interviews with twice that many prospective witnesses for Mr. Jordan to be cleared. That is an expensive way for the government -- and for Mr. Jordan, who felt compelled to hire a lawyer to defend his interests and reputation -- to dispose of charges that would have been laughed off if they had been leveled at an ordinary citizen.

While Mr. Jordan has been vindicated, the Ethics in Government Act has not been. This kind of searching inquiry into the validity of what were clearly petty and self-serving allegations was not what the country had in mind when passage of that act was widely hailed.

The act, which sets up the mechanism requiring FBI investigations, special prosecutors et al., was designed to handle charges that high government officials had committed serious crimes. But its language says its procedures take effect when any high official is alleged to have violated any federal law. It was irrelevant that the crimes Mr. Jordan was said to have committed were misdemeanors that the Department of Justice seldom prosecutes and even less frequently investigates.

There is, of course, an escape valve in the act. It permits the attorney general to terminate such an investigation if he decides the charges are frivolous.Some, perhaps many, attorneys general would have used that provision to end the Jordan affair six months ago. But Benjamin R. Civiletti is a particularly prim prosecutor who interpreted the law strictly. He said he could not call the charges frivolous because two key witnesses refused to talk to him.

As a result, the affair ground on to its ultimate conclusion -- the 53-page report to a special three-judge court and a secret addendum that was sent to Mr. Civiletti. That addendum presumably contains the evidence on which he will now have to decide whether perjury was committed when the original charges were made against Mr. Jordan.

The country cannot tolerate having serious charges against high officials covered up or left uninvestigated and, if the Jordan affair has any beneficial aspect at all, it demonstrates that the Ethics in Government Act narrows the possibility of such coverups. If something so inconsequential throws the act into gear, then surely charges would also be taken up. But the country also cannot tolerate having its high officials bear unnecessarily the kind of burden under which Mr. Jordan has worked for the last nine months. There should be a better process for screening out fundamentally frivolous charges.