The answer has enormous consequences both for the victims - they won a nearly $315 million default judgment against the Republican of Sudan - and apparently for the U.S. government, which said a ruling against Sudan could harm international relations and endanger the government's legal position in the world.
At issue was a directive in the Foreign Sovereign Immunities Act that notice of any legal action against a foreign government be "addressed and dispatched" to the head of that country's ministry of foreign affairs.
Lawsuits against Sudan for providing material support for the al-Qaida attack were sent to the Sudanese embassy in Washington. But Christopher Curran, a Washington lawyer representing Sudan, told the court that they should have been sent to the foreign minister's office in Khartoum.
If Curran is right, the judgments against the country would be vacated.
One appeals court has looked at the question and decided mailing a notice to the embassy was fine. Another has sided with Curran.
The justices seemed similarly divided.
"I have to say . . . that would be my first thought: Why don't I deliver it to the embassy," said Chief Justice John Roberts Jr. "Mailing it to the foreign minister in some country and assuming it's going to get there in any reasonable time, I think you're much more likely to reach them through the embassy."
But Curran said the foreign minister does not have an office at the embassy. "So it literally would not be complying with the statutory language to send the mailing to that diplomatic mission," he said.
Justice Elena Kagan said there is no language in the statute that says it must be addressed to the foreign minister's office. "Everybody understands that embassies are supposed to be the point of contact if you want to do anything with respect to a foreign government," she said.
Justice Samuel Alito Jr. was also a tough questioner. He noted the law was written before the "era of FedEx" and wondered whether it was really so simple to send a package with a "Return Receipt Requested and it comes back from the far reaches of the world?"
Curran responded that what is known is that Congress decided not to require that such notices be filed with embassies because countries objected to that.
Department of Justice lawyer Erica Ross backed him up, saying service at embassies could violate the Vienna Convention on Diplomatic Relations, which says that the premises of an embassy be "inviolable."
But what practical harm does the U.S. see in mailing notices to an embassy, asked Justice Brett Kavanaugh.
"The harm is that the United States has embassies all over the world, obviously, and sort of deputizing each of those to accept service on behalf of the United States is quite problematic," Ross said.
The deadly Oct. 12, 2000, attack on the Cole, when it was refueling at a harbor in Yemen, killed 17 American sailors - 15 men and two women - and wounded 42 others. Washington lawyer Kannon Shanmugam represents the families of the dead and those wounded.
He said it would be wrong to throw out the judgments they had received because of an "unstated procedural requirement."
But he faced hard questions, too.
Justice Sonia Sotomayor said the "addressed and dispatched" language implied a sense of urgency to make sure it got to the foreign minister, rather than mailing it to the embassy in the U.S.
"We can't ignore that it's not the place where the person usually is," she said. "And that concept, I think, is the essence of due process."
Justice Stephen Breyer said research by his clerks showed two dozen countries, like the United States, does not accept legal notice at their embassies. "I could find nothing the other way" that would support Shanmugam's position, he told the lawyer.
Kavanaugh was also concerned. "The point you're making is it's not a big deal to allow service at an embassy, even though the United States objects and even though, as Justice Breyer points out, no other country appears to allow that."
Alito and Justice Ruth Bader Ginsburg had a practical concern: did the mailing at the embassy actually give Sudan notice of the suit?
"Sudan unquestionably had actual notice of the litigation," said Shanmugam, and decided not to show up. It was only after the victims had won a default judgment and were attempting to access Sudanese assets held in New York banks did Sudan file its objections, he said.
Curran was circumspect when he was asked. He said there was "nothing in the record" to indicate the Sudanese foreign minister received the notice sent to the embassy, although an employee signed for it. Under further questioning, he acknowledged that Sudan had notice of the suit sometime before the default judgment was filed.
If the court rules for Sudan, the judgment for the families is likely thrown out, and the legal process must begin anew. In that case, "Sudan is committed to appearing and defending itself," Curran told Alito. "It believes that the default judgment was ill-founded. It has substantial defenses and it would like to contest the charges."
The case is Republic of Sudan v. Harrison.