The reason is the growing speculation that the new and seemingly moderate president of Iran, Hassan Rowhani, might actually shake hands today with U.S. President Barack Obama inside the UN, which Rowhani is scheduled to address.
That simple handshake, if it happens, will be the highest official contact between these two proud nations in over 30 years of bitter deadlock.
Not quite the same surprise, perhaps, as Richard Nixon flying to Beijing to open relations with Communist China in 1972; or then Egyptian president Anwar Sadat arriving to address the Israeli parliament in 1977.
But it would certainly be a well-choreographed statement that the time is ripe for profound change for a region and a moment in history when optimism is desperately needed.
It would also be a sea change from the grim mood of mutual suspicion and loathing that has surrounded most Iranian forays into international affairs in recent years.
Even if these two leaders don't physically meet, the smooth Iranian leader — dubbed "the silky Mr. Rowhani" by The Financial Times — is expected to redouble his charm offensive aimed at quickly ending Iran's long and debilitating isolation as a pariah nation.
He has already released a spate of political prisoners, bid the Jews of the world Rosh Hashanah greetings, and has been talking more openly about an international accommodation on Iran's nuclear plans.
And given that that he and Obama have already exchanged at least some personal correspondence on the prospects of better U.S.-Iran relations, this is one offensive Obama will surely welcome. Albeit with a careful show of skepticism.
For the very possibility of an actual detente with Iran, following the Islamist revolution in 1979 that kept 52 Americans hostage for 444 days, rather takes the collective breath away.
To be successful, of course, such a detente would have to end the long stalemate over Iran's nuclear intentions.
This can only be done if Iran can satisfactorily open all nuclear materials and enrichment plants to exacting international inspection to prove its repeated pledge that it seeks to build no atomic weapons.
Should this succeed, the extremely tough international sanctions that the U.S. has spearheaded, to the point of cripplingly Iran into an almost full depression, would be ended.
Secondly, it appears Washington is already imagining scenarios in which a quick detente might lead to Iran helping achieve a negotiated settlement to the Syrian civil war.
Iran, which finds itself increasingly an outcast in the Middle East because of its unpopular support of Syria's Assad, now appears anxious to work alongside ally Russia to help end the fighting.
It has ample reason to want peace. Iran is believed to be providing Assad with $9 billion a year in arms — a sacrifice its weak economy can ill afford. But that also means it has rare leverage over Damascus, which Rowhani appears ready to use.
For the gravest danger of the Syria war is that it seems on the verge of setting off a general conflagration between Shia Muslims, which Iran represents, and the Sunni majority in the region.
The longer the war lasts, the more isolated Iran becomes and the more dangerous the risks of an all-out religious conflict.
Today, the hard-liners no longer seem in full control in Iran. But there is also ample room for caution.
Both Israel, which portrays Rowhani as "a wolf in sheep's clothing," and Saudi Arabia, both key allies of the U.S., warn that Iran has no intention of foregoing nukes and through them, its goal of regional hegemony.
Others make the point that even if Rowhani represents a truly moderate break with the country's past fundamentalist leadership, the real power still lies with the supreme leader, Ayatollah Ali Khamenei, and the always hawkish Republican Guard — meaning Iran could shift course again at any moment.
Against the outright skeptics, however, cautious optimists note that Khamenei and Rowhani have a long-standing political relationship, and that the new president has been given clear assurances the supreme leader backs both his direction and his policy team, including the worldly and moderate foreign minister, Mohammad Javed Zarif.
Rowhani's somewhat surprising election last summer showed widespread discontent against the old order.
In an early move, the new president boldly switched control of the nuclear issue from the hardline National Security Council to the foreign ministry, and ordered the Republican Guards to stay out of politics.
More to the point, Rowhani is taking pragmatic steps that even many conservative voices concede are necessary in order to free Iran from the devastating economic sanctions imposed by the nuclear standoff.
And while Iran does not like its isolation, it has been even more shaken by a 45 per cent fall in oil revenues and a similar plunge in industrial production over the past couple years, which has created what the government concedes, is a "tsunami" of 8.5 million unemployed.
Given this damage, Iran may well feel there's little risk in abandoning nuclear weapons at this juncture.
That effort, after all, was at least in theory designed to block a future U.S. land invasion of Iran similar to what took place in Afghanistan and Iraq. But that whole era seems to be ending in any case as Americans sour on foreign wars.
So, Rowhani must be asking himself what would Iran gain by producing such weapons now. Even if it were to be successful, and avoided Western air attacks, it would face a long Cold War-style "containment" by the West and Israel as it sank further into national poverty.
On the other hand, if its long-sealed diplomatic doors are pried open, Iran has a chance to re-emerge as a respected and prosperous power in the Middle East.
Given the state of perpetual crisis in the region, the existence of even a "chance" for a breakthrough surely requires bold leaders to move in to test the waters, with at least some urgency.