The US Supreme Court is considering an appeal by the parents of an unarmed Mexican teenager who was killed by a US border patrol agent.
Agent Jesus Mesa was on the US side when he fatally shot Sergio Adrian Hernandez Guereca, 15, across the Mexican border in June 2010.
Agent Mesa was not prosecuted or extradited to face criminal charges.
The case could determine the scope of US law and whether non-citizens are protected by American courts.
During oral arguments on Tuesday, the eight US judges appeared evenly divided, with the conservative-leaning jurists saying that the fact that the teenager's death occurred in Mexico should be reason enough to keep the case out of US courts.
But the court's liberal judges indicated they may support the parents' ability to sue based on the death occurring in an area where both the US and Mexico share legal responsibilities.
Agent Mesa was on a bicycle patrol between El Paso, Texas, and Juarez, Mexico, when he shot and killed the Mexican boy.
Sergio was among a group at a cement culvert by an 18ft (5.4 metres) high border fence when Agent Mesa tried to apprehend them.
The officer caught one of the boys while two others on the Mexican side ran and hid behind a pillar.
The teenager's family said he was just playing with friends.
But the Justice Department said the officer was trying to stop "smugglers attempting an illegal border crossing".
Agent Mesa said in court documents that he opened fire after rocks were thrown at him from across the border, including by Sergio.
Mobile phone footage showed that Sergio was struck as he peeked out from behind a pillar, according to the petitioner's brief.
US officials decided against prosecuting Agent Mesa, arguing the Justice Department lacked jurisdiction on the Mexican side of the border.
Though Mexican officials charged Agent Mesa with murder, the Obama administration refused to extradite him.
The teenager's parents sued Agent Mesa for damages, but lower courts dismissed the lawsuit. The Supreme Court agreed to take up the case in October.
The case comes in the wake President Donald Trump's order for the "immediate construction" of a border wall and the hiring of an additional 5,000 border patrol agents.
The teenager's death is not the only border case facing legal challenges.
The parents of a teen killed in Nogales, Mexico, by a US agent across the border have filed a civil rights lawsuit, which is pending until the Supreme Court issues a ruling.
Prosecutors are pursuing second-degree murder charges against Agent Lonnie Swartz in the death of 16-year-old Jose Antonio Elena Rodriguez.
A 2013 report, commissioned by US Customs and Border Protection and written by an independent group, found that the agency failed to sufficiently investigate 67 border shootings between 2010-12.
The report also questioned the use of force in some of those cases.
The agency has said it has since changed it policies, including response to reports of rock-throwing.