When Donald T. Regan takes over today as White House chief of staff, he will be operating in a difficult environment where the stopwatch of history has begun to tick.

While Regan has proven an able secretary of the treasury, few have taken the reins of the White House staff under less auspicious circumstances.

The 66-year-old former stockbroker inherits what may be the toughest job in Washington at a time when Reaganism is at its crest and bitter and divisive battles on spending cuts, tax simplification and arms control lie dead ahead.

President Reagan is enjoying a level of popularity higher than any chief executive since Dwight D. Eisenhower, but Republicans on Capitol Hill are increasingly restive on a wide range of economic and foreign policy issues. The GOP's congressional wing and the White House seem on a collision course on the defense budget, which will have to be cut far more than Reagan and Defense Secretary Caspar W. Weinberger desire to win Democratic support for slashes in domestic spending.

It is also far easier to follow a bad act than a good one, and Regan will be succeeding an especially adroit presidential chief of staff. Plenty of Reagan conservatives complain that James A. Baker III pushed the president's agenda leftward, but few question his competence or political skill.

Regan also is taking over with an extremely limited start-up time. The job swap with Baker may turn out to be a better idea than it seems, but Regan should have been given three months, not three weeks, to find his moorings and replace the competent people Baker is taking with him to Treasury.

Like his boss, Regan is committed to corporate ideals of governance. Both men have compared the White House to a gigantic firm in which the chief of staff serves as chief operating officer and the president as chairman of the board.

But the corporate model is a deficient description of a presidency that has more often resembled a group of feuding fiefdoms than a corporation.

The so-called press leaks that have distressed the president were a byproduct of this feuding, which took its toll on the participants but, on balance, benefited Reagan.

Profound differences among his subordinates forced Reagan to become involved and informed on issues that he would otherwise have been inclined to delegate. As a consequence, he knows far more about deficits and the defense budget than he would have been compelled to learn in a more hierarchal White House.

But it is corporate order to which Regan now aspires. He has made it known that he considers "leaks" equivalent to mortal sin and will do his best to prevent them.

Such proclamations curry favor with the president but do him no service. The fact is that some of the "leaks" about which Reagan has become most alarmed were used by his aides to test public and congressional reaction to controversial policies.

The "leaks," for instance, that U.S. forces would be withdrawn from Lebanon or that Anne M. Burford would be replaced as head of the Environmental Protection Agency helped to produce support for these decisions while they were being debated and to bring them to reality. These leaks were a help, not a hindrance, to Reagan.

Beyond the "leaks" issue, the question remains whether Regan's talents are suited to his new post. He is brainy and determined, but an official who knows Regan well describes him as deferential to the president, collegial to his peers and tyrannical to his subordinates.

This sounds more like a description of a disaster than a chief of staff. In the White House, as some of its occupants have learned the hard way, deference comes automatically, while messengers willing to bring the bad news are rare commodities.

Regan bridles at the suggestion that he is a "yes man," and indeed this is the sort of canard that gains currency, makes the rounds and becomes accepted as fact without requiring evidence in its behalf. He deserves a chance and a presumption of good will.

But Regan ought to start by recognizing that he will be a very prominent target and a strongman in a White House that, through a combination of accident and design, has been relatively competitive and open in its processes during the first term. He should realize that this openness was an ingredient of Baker's success.

In talking to colleagues, Regan has sometimes compared himself to an organ player, saying: "Everyone can see his hands, but no one knows what his feet are doing." That's not a bad description of Regan's new job, but he is going to need some very fancy footwork to succeed.

Reaganism of the Week: Chatting with savings and loan executives last Monday, Reagan said, "I don't have birthdays anymore."