THIS IS INCREDIBLE: Mrs. Augusto Pinochet, wife of the general who led the coup against the government of Chile in 1973 and who has run a tight and nasty military dictatorship since, is received for tea in the Reagan White House. Mrs. Salvador Allende, widow of the elected president who was deposed and killed in that coup, is now refused a visa to enter the United States to give a speech.

And why is Mrs. Allende denied the opportunity to say what's on her mind to the people in California who invited her? It would be, says a State Department spokesman, picking up language in the immigration law, "prejudicial to U.S. interests." What might that mean? Well, for one thing, as she acknowledges, Mrs. Allende has had something to do with the Soviet-connected World Peace Council and for another, as she also acknowledges, she is likely to say some harsh words about the Chilean government--the government, you will recall, responsible for killing her husband and for much else.

We have another view of what is "prejudicial to U.S. interests": barring an invited foreign guest for arbitrary and petty reasons, preventing her from presenting her wares in the political marketplace, keeping those Americans so inclined from deciding for themselves the merits of what she has to say, and shaming the United States in the eyes of democratic-minded people around the world.

So what if Mrs. Allende belongs to the Grandmothers for Marx Federation? So what if she says some harsh things about the Reagan administration's continuing efforts to bring the Pinochet regime back into the American fold? There is also the obvious fact that the denial of the visa ensures Mrs. Allende and her ideas a measure of sympathy and celebrity otherwise beyond her reach.

It's not unreasonable that the immigration law should provide the government some authority to pass on aliens who come and go. We happen to think the authority in the law is too broad, but no early narrowing is likely. Nevertheless, the government can administer the law with some judgment and restraint. In this case, the administration has shown neither.