May 28 (Reuters) - U.S. and Iranian officials began rare talks in Baghdad on Monday to discuss Iraq's spiralling violence, which Washington says Tehran is fuelling by giving arms, funding and training to Shi'ite militias there.

Here is a chronology of major events in Iran-U.S. relations:

August 1953 - CIA helps orchestrate the overthrow of Iran's popular Prime Minister Mohammed Mossadegh, restoring the shah of Iran, Mohammed Reza Pahlavi, to power.

Jan. 16, 1979 - Pahlavi is forced into exile after mounting discontent with his authoritarian rule.

-- Feb. 1 - Ayatollah Ruhollah Khomeini triumphantly returns to Tehran after some 15 years in exile.

-- October - The U.S. allows the shah to enter the country for medical treatment, angering the revolutionary government.

-- Nov. 4 - Iranian students seize the U.S. embassy in Tehran and take 90 hostage; 52 held captive for 444 days.

April 7, 1980 - U.S. President Jimmy Carter breaks off diplomatic relations with Iran.

-- April 25 - A U.S. commando mission to rescue the embassy hostages fails in the desert, killing eight Americans.

-- Sept. - Iraq invades Iran to lay claim to Shatt-al-Arab waterway. Washington supports Iraq in war that lasts until 1988.

Jan. 20, 1981 - American hostages are released on the day of Ronald Reagan's inauguration as U.S. president.

1986 - President Reagan admits secret arms deal with Iran in breach of the U.S. arms embargo. Money from the sales was secretly passed to Contra guerrillas in Nicaragua.

July 3, 1988 - U.S. warship Vincennes mistakenly shoots down an Iranian passenger plane over the Gulf, killing 290 on board.

March 16, 1995 - U.S. President Bill Clinton issues executive orders preventing U.S. companies from investing in Iranian oil and gas and from trading with Iran.

Jan. 29, 2002 - U.S. President George W. Bush accuses Iran, Iraq and North Korea of being an "axis of evil."

June 2003 - International Atomic Energy Agency says Iran has failed to comply with nuclear Non-Proliferation Treaty.

February 2005 - President Mohammad Khatami says no Iranian government will give up nuclear technology programme.

August 2005 - Mahmoud Ahmadinejad becomes president of Iran.

May 31, 2006 - Washington says willing to join multilateral talks with Iran if it verifiably suspends its nuclear programme.

Sept. 30 - U.S. Congress agrees to extend economic sanctions on Iran for another five years.

Dec. 23 - United Nations imposes sanctions on Iran in an effort to stop nuclear enrichment work.

Feb. 8, 2007 - Supreme Leader Ayatollah Ali Khamenei says Iran would target U.S. interests around the world if it came under attack over its nuclear programme.

Feb. 26 - Major powers agree to begin work on a new U.N. Security Council resolution on Iran.

March 10 - U.S., Iranian officials attend meeting in Baghdad aimed at stopping the spread of sectarian violence in Iraq.

May 2 - Ahmadinejad calls on U.S. and other foreign forces to leave neighbouring Iraq, reiterating an Iranian demand on the eve of an international meeting in Egypt.

May 28 - Iranian and U.S. ambassadors to Iraq meet in Baghdad to discuss violence in the country.

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