THE REQUEST of Chang Sungnam for political asylum in the United States is an especially compelling one. He is a South Korean journalist who insists, probably quite accurately, that he would be subjected to political persecution if he returned to his homeland. In addition, since he first requested asylum in 1974, he has developed an inoperabel stomach cancer. Yet, it took the U.S. government three years to act on his request, and it did so then only in very strange fashion. Early in August, the Immigration and Naturalization Service denied Mr. Chang asylum - despite a contrary recommendation from the State Department. Later in the month, after a review of his case at a higher level in the Immigration and Natularization Service, he was granted asylum for one year. At the end of the year, the INS explains, the case will be considered again, in light of the conditions in South Korea at that time, and his period of asylum will be ended, extended or made permanent.

It is easy to understand why a case involving political repression in a nation that is closely allied with the United States raises difficult questions in the bureaucracy - although why this particular case took three years to resolve remains a mystery. And it is easy to understand why the Immigration Service has sometimes granted political refugees the right to remain in this country under labels other than that of asylum. Many governmnets regard the granting of asylum to their nationals as an embarrassing or unfriendly act, carrying with it - or so it seems to them - an official denunciation of the way they run their countries. Thus it is tempting to grant political asylum readily to refugees from unfriendly countries and to look quite skeptically at the applications of those friendly countries.

President Carter's human-rights campaign, however, has undermined that approach to the whole matter of political asylum. It can hardly be possible that the granting of asylum to one South Korean or more would be considered by Seoul more embarrassing or unfriendly than the President's publicly spoken concern about the repression of human rights there. Indeed, such action would add some degree of force and credibility to the President's admonitions, for it would mean this country was backing up his high-sounding statements with specific acts.

The granting of asylum, of course, is a tricky business, involving difficult distinctions between legitimate requests and those made simply to get around immigration limitations. But Mr. Carter's global human-rights crusade also simplifies the decision making, if he means to be truly global about it, by making it possible to treat all legitimate requests on the same basis, instead of looking at some - those from Communist countries, for example - in a more favorable light than others. That is as it should be. And it strengthens immeasurably the already strong case for granting asylum to Chang Sungnam.