SUDDENLY the Reagan administration is deep into the crisis in Chad, where insurgents backed by Libya, a radical Soviet client state, are pressing the government hard. Three military advisers are on the ground, the fleet is being shown off Libya's Mediterranean coast, AWACS surveillance planes are on the scene and some millions of dollars are on the way in various forms of military aid. It adds up to a conspicuous investment of American power and prestige in a country in which the United States has no traditional interests to speak of and which, we expect, very few Americans could find on a map. The intervention comes at a moment of intense debate over the administration's policies in Central America. It cannot help the president's position in that debate. It is more likely to hurt it.

What is the United States doing in Chad? The basis of the administration's response is the menace it continues to perceive in Libya's Col. Qaddafi, who has put his oil money at the service of an extravagant ambition and a radical ideology. We do not underestimate Col. Qaddafi. He has posed, and still poses, real dangers across a wide swath of African and Middle Eastern states--for years he has made trouble for and in Chad. His machinations led him repeatedly to be rejected by his fellow Africans when it came Libya's turn to fill the presidency of the Organization of African Unity. The Soviets have loaded him up with billions of dollars in weapons, confident that he can do a great deal of harm.

To accept that Col. Qaddafi is a menace, however, is not to agree that the United States should be leading the fight against him. Chad is not familiar, let alone vital, American turf. For the patronage that most of the small African states still seek from the West, Chad looks first to France, the former colonial master, as Secretary of State George Schultz underscored yesterday. The French do remain involved there. The trouble is that the Socialist government of Francois Mitterrand has not entirely shed the posture of opposition to "neo-colonialism" that it acquired in its long years in the political wilderness. As a result it has been slow to act on what many Africans accept as the traditional French responsibility in Chad. Yesterday's statement by the French minister of defense was a case study in hestitation.

Libyan planes are reported to have been bombing targets in Chad, and Libyan troops have reportedly crossed the border. Chad cannot be faulted for seeking foreign help. But will the American response make it more or less likely for an active role to be taken by France and by those of Chad's neighbors with a more direct interest in the outcome?