By Norma Percy
Series Producer, Iran and the West
Obama hopes to succeed where other US Presidents have failed
President Barack Obama offered to "extend a hand" of diplomacy if the Islamic Republic's leaders would "unclench their fist."
But can he succeed in improving relations when all previous attempts at talks between Iran and the West have ended as the dialogue of the deaf?
It is 30 years this week since the Shah of Iran was overthrown and the Islamic Republic of Iran was established under Ayatollah Khomeini.
Relations between Washington and Tehran took a disastrous turn at that time and the two sides have barely been on speaking terms ever since.
For Iran, the historical mistrust went back further. The last time the Shah had been deposed - in 1953 - the US and Britain staged a coup and returned him to power.
So when, soon after the 1979 revolution, President Jimmy Carter admitted the Shah, who had terminal cancer, to the US, alarm bells were already ringing in Tehran.
Ayatollah Khomeini's legacy still overshadows US-Iranian relations
Iran's former Foreign Minister, Ibrahim Yazdi recalls meeting President Carter's National Security advisor Zbigniew Brzezinski to explain the problem - that the action was provoking memories of 1953. "No matter what you say the Iranian people will never accept this - they cannot swallow it."
Days later, a group of students seized the US Embassy in Tehran, demanding the Shah be returned to face trial.
Their action was backed by Iran's new leader Ayatollah Khomeini - and US-Iran relations fell to a new low as more than 50 people were held hostage for a total of 444 days.
Such was the mistrust of Iran's new regime, that in the 1980s the US and Britain backed Saddam Hussein's Iraq as a counter to Iran's influence in the region.
American actions have often seemed in Tehran to be designed to provoke. And perhaps the most remarkable example is the American response to Saddam Hussein's use of chemical weapons during the Iran-Iraq war in the 1980s.
"It was a violation of the Geneva Convention. But members of the Security Council did not see it as in their interest to cross Saddam Hussein," says Perez de Cuellar, UN Secretary General at the time.
The US and Britain continued to back Iraq militarily and politically to the closing days of the war.
"You want them to stop using the chemical weapons," George Shultz, then President Reagan's Secretary of State, explains.
"At the same time, you don't want to see Iran win the war."
Mr Obama is not the first US President to turn his attention to Iran in the opening days of his presidency.
I showed goodwill first - the Americans broke their promises
Former President of Iran, Hashemi Rafsanjani
President Bush Senior's words in his 1989 inaugural address, "Goodwill begets Goodwill" were addressed to Iran as the US was desperate to secure the release of American hostages - this time held in Lebanon by Hezbollah - and knew Iran could fix it.
Iran's new President Rafsanjani decided to take a huge risk. He sent the leader of the Revolutionary Guard to Lebanon and the Western hostages in Lebanon were duly released.
Mr Rafsanjani waited eagerly for the reciprocal "goodwill" which President Bush had promised. He got nothing.
Bruce Reidel, who was working for the CIA at the time, explains the American thinking: "The Iranians were now deeply engaged in other acts of terrorism that made it very, very hard to do anything to improve the relationship."
The US blamed Iran for the murder of a dozen Iranian exiles in the West and the destruction of the Israeli embassy in Buenos Aires and there was the fatwa from Iran's Supreme Leader ordering Muslims anywhere in the world to kill Salman Rushdie.
President Rafsanjani felt let down. "I showed goodwill first. The Americans broke their promises," he says.
For his remaining five years as president, he felt unable to risk public opinion at home and make any further attempts to open doors to the West.
So the next attempt at rapprochement had to wait for a new Iranian president. In 1997 President Mohammad Khatami announced: "I would like to talk to the people of America and, God willing, at the right time, I will."
Risking the wrath of Iran's dominant clerical establishment, he began cautiously with a "people to people policy", the visit of a US wrestling team to Iran.
The US saw the opportunity, but before President Bill Clinton could reciprocate, the FBI found evidence which they said proved Iran had been behind another terrorist attack - a truck bomb at Khobar Towers in Saudi Arabia which killed 19 US servicemen, a year before Mr Khatami was elected.
Mr Clinton's Secretary of State Madeleine Albright explains the problems this created in Washington: "The question was how to separate Khatami out from previous actions and not hold him responsible."
Mr Clinton wrote to Mr Khatami asking him to take action against the Iranians who were responsible.
But the attempt was doomed to fail. President Khatami could not act without the support of Iran's Supreme Leader, even if he had wanted to.
In fact, Mr Khatami still insists Iran had nothing to do with the bombing.
"The Americans did not understand the situation in Iran. They made big mistakes. They destroyed the ground that had been prepared to re-establish ties," he says.
But then came 9/11. In Afghanistan, Iran and the West suddenly had an overwhelming common interest. "The Taleban and their instrument, al-Qaeda were our enemy," Mr Khatami says.
"America now thought the Taleban was their enemy. So if they toppled the Taleban, Iran's national interest would be served."
"When the Taleban occupied Afghanistan they talked about an Islamic State, but they meant rule by a Sheik and an Emir, not a president. And they are narrow-minded about women in society. The Taleban believed and still believe that Iran is an enemy," Mr Khatami adds.
Iranian and American officials began meeting in New York and Geneva, to swap intelligence and coordinate policy.
One of the Iranian officials unfurled a map on the table and pointed to the targets the US needed to focus on, particularly in the North. It led to a swift victory in the US bombing campaign.
But America was not willing to proceed jointly on to the next common interest, Iraq.
Mr Obama says he is prepared to open talks with Iran without preconditions, declaring in his inauguration speech: "To the Muslim world, we seek a new way forward, based on mutual interest and mutual respect."
Can it work? What are the lessons from the past? Obama's team need to understand what Iranians see as grievances - whether they are legitimate or not.
Iran and the West, produced by Norma Percy is on BBC Two on Saturdays at 21:00GMT on 7, 14, 21 February, repeated Thursdays 23:50GMT. Viewers in the UK can also watch on BBC iPlayer.
Contributors to the series include Former US President Carter, Former Presidents of Iran Khatami and Rafsanjani, Former UN Secretary-General Perez de Cuellar, Former US Vice President Walter Mondale, Former US Secretaries of State Madeleine Albright, Warren Christopher, George Shultz, Former British Foreign Secretary Jack Straw, and Former German Foreign Minister Joschka Fischer.