A 2002 law says yes, but the State Department says no. That led to a lawsuit by parents of an American boy named Menachem Zivotofsky, who was born in a Jerusalem hospital soon after the law was passed. The United States has refused to recognize any nation's sovereignty over Jerusalem since Israel's creation in 1948, so the boy's U.S. passport only says "Jerusalem" as his birthplace.
The Bush administration said Congress may not tell the president what to do regarding this aspect of foreign relations, and the Obama administration has taken the same position. The court is looking at whether the 2002 law impermissibly infringes on the president's constitutional powers. The hearing came on the same day that President Barack Obama heads to Israel for his first visit there as president.
The State Department argues that designations on passports must accurately reflect U.S. positions on recognition and borders.
"How can we second-guess the president on that?" asked Judge David S. Tatel, who did the bulk of the questioning for the three-judge panel of the U.S. Court of Appeals for the District of Columbia Circuit.
The attorney for the Zivotofskys, Nathan Lewin, responded that Congress has determined that the State Department policy "makes no sense.
There is "no real interest on the other side," Lewin argued.
But Tatel, an appointee of Democratic President Bill Clinton, said that he didn't understand how Congress declaring the U.S. policy made no sense fit in to the court's review.
"How do we write, 'the policy is irrational?'" Tatel asked.
The same way, Lewin said, as if the president said he wouldn't allow people to identify themselves as having green eyes on passports.
Judge Karen LeCraft Henderson, meanwhile, wondered how far Congress could go in dictating foreign policy.
"If Congress says it's wrong to negotiate with a country, could it do that?" asked Henderson, who was appointed by Republican President George H.W. Bush.
The U.S. and most nations do not recognize Jerusalem as the capital and say the city's status should be resolved in negotiations between Israel and the Palestinians. The U.S. keeps its embassy in Tel Aviv.
The 2002 law was part of a large foreign affairs bill that President George W. Bush signed into law. But even as he did so, Bush issued a signing statement in which he said that "U.S. policy regarding Jerusalem has not changed."
Justice Department lawyer Dana Kaersvang, arguing on behalf of the State Department, said that a passport is a diplomatic instrument. But she got some pointed questions as well.
Tatel said he could understand the problem if a person's passport said "Jerusalem, Israel," but wondered what the harm would be to U.S. foreign policy in having someone born in Jerusalem identify Israel as their birthplace.
"Nobody will know" that they were born in Jerusalem, he said.
Kaersvang said that the president is owed deference in foreign affairs, but Tatel said the court's role is not just to stamp it and "and say fine. It has to make sense."
Kaersvang argued that the issue is consequential.
"When Congress passed this statute, it was greeted with uproar in the Middle East," she said.
Tatel noted that the State Department argues that the law encroaches and interferes with the president's foreign policy, but asked, "How do we know that this has crossed the line?"
The lawsuit was filed back in 2003, and a judge said it was a political question for Congress and the president to work out without the intervention of the courts. A three-judge appeals court panel - made up of different judges than the panel hearing the case now - agreed that it had no authority to consider the claim.
But the Supreme Court last year overturned the ruling and sent the case back down to the appeals court to decide whether the law was constitutional.