Terrorism came to Washington once again yesterday. The chaos and violence of world events crystallized in an instant in a Bethesda home as a gunman pumped bullets into the stomach of Ali Akbar Tabatabai.

The slaying of the former press attache at the Iranian Embassy here, like the assassination here of ex-Chilean Ambassador Orlando Letelier in 1976 and Israeli Col. Yosef Alon in 1973, is yet another incident of international terrorism that both complicates U.S. foreign policy and demonstrates that Washington is not immune to the type of political violence that has affected so much of the rest of the world.

In the Letelier case, the apparent connivance of the Chilean government in the assassination and its refusal to extradite three Chilean intelligence officers charged with the crime exacerbated the strained relations between Chile's military government and the Carter administration, relations already under pressure because of the U.S. efforts to promote human rights internationally.

Col. Alon -- like Tabatabai shot dead at his Bethesda home -- was the Israeli air and naval attache here. The crime was never solved, but Arab terrorists claimed responsibility for it. Like the Munich massacre of Israeli athletes in 1972, Alon's death went down in history as an item in the worldwide terrorist struggle between the Arabs and Israelis, a struggle whose intensity and constant recurrence undermines the continuing diplomatic efforts to bring peace to the Middle East.

Tabatabai's slaying yesterday is not the first violence here connected with the Iranian revolution -- there have been student demonstrations accompanied by violence. But it is the first to have that premeditated, almost professional quality that immediately raised questions here yesterday about whether the current Iranian government. of whom Tabatabai was an active foe, may have played any role.

Should such a link be established, it would add yet another complication to the tensions resulting from Iran's having held American hostages for almost nine months.

"If what we're seeing is transnational terrorism, where the shots are being called by another nation using their own operatives, then that is indeed the long arm of terrorism reaching here," said Dr. Frank Ochberg, a psychiatrist who is specialist on terrorism. Ochberg is director of the Michigan department of mental health and is training police department and FBI negotiators on tactics for dealing with terrorists in hostage situations.

An FBI official cited "the seeming professionalism of the assassination," but investigators had no clues yesterday linking the slaying to the Iranian government.

A State Department spokesman said, "We do not know what the motives were in this case."

The Tabatabai slaying comes just days after former Iranian prime minister Shahpour Bakhtiar escaped an assassination attempt in Paris last Friday in which a policeman and a next door neighbor were killed.

In that case, three would-be assassins posed as journalists. Investigators yesterday pointed out the similarity of this ruse to that of the Tabatabai assassin who posed as a postman.

Experts in international terrorism like Ochberg said yesterday there may be significance in the assassination's taking place in a suburb of the nation's capital.

"It may well be a political statement to do it in Washington," said Robert Kupperman, a member of the Georgetown University Center for Strategic Studies and a private consultant on issues of national security and terrorism. "The U.S. appears weaker since Iran took U.S. hostages and the inhibitions that were around against assassinations in Washington may not be around any more."

The Letelier and Alon Assassinations happened here in the past decade, but Kupperman said these added up to relative tranquility compared with the rash of violence and assassinations that swept across Europe, the Middle East, South America and other parts of the world during the same period.

"I think there is a perception that the U.S. has a higher tolerance for chaos and violence than ever before," Kuperman said. " . . . We're in for an age of terror and unconventional warfare. If we appear to be paralyzed in Iran, I suspect we invite more and more of it."

Ochberg said that the United States has been "lucky" to have had so little terorism in the past decade, but he said that this may change and that yesterday's asassination may pyschologically encourage further violence.

"Many of us (experts on terrorism) have said it's going to happen in the U.S. No country is unassailable," Kupperman said.

Besides the assassinations, a secretary in the British Embassy here lost her hand when a letter bomb exploded in 1973, an act of violence attributed to the Irish Republican Army.

On March 9, 1977, Hanafi Muslims seized 134 hostages at three locations, killing a radio reporter and wounding several people, including then-City Councilman and now Mayor Marion Barry. Although the incident resulted from a squabble with Black Muslims in the United States, it had broader implications because of anti-Semitic statements by the Hanafis and their Muslim affillatioin and because one of the sites seized was the B'nai B'rith headquarters in downtown Washington.

In November 1977 thousands of Iranian demonstrators flooded Washington to protest the shah's regime, and their clashes with the police led to injuries to 96 demonstrators and 28 police officers.