Oregon voters approved the law in 1934, when the Ku Klux Klan was a powerful influence in the state and anti-immigrant sentiment was high. The measure applies only to felonies that are not first-degree murder cases.

Legal experts say that allowing nonunanimous convictions raises the risk that jurors from racial, ethnic or religious minorities will be ignored by a majority that knows it can return a verdict without them — thereby denying the jurors a fair hearing and the defendants a fair trial. Oregon’s population is about 85 percent white, and most people convicted by nonunanimous juries there are white as well. But Aliza B. Kaplan, director of the Criminal Justice Reform Clinic Oregon at Lewis & Clark Law School in Portland, who has studied the history of nonunanimous juries, said the impact of the law in an overwhelmingly white state is that racial minorities rarely have juries of their peers.

If the Supreme Court rules that divided jury verdicts violate the Sixth Amendment guarantee of a fair trial, Oregon might be forced to rethink large parts of its criminal justice system, including jury instructions, lawyers’ tactics when picking jurors — as well as potentially thousands of previous convictions by divided juries.

Victims’ rights groups in Oregon say they also have concerns that ending nonunanimous jury convictions would lead to far more hung juries and mistrials, forcing victims to testify multiple times.

Erin Greenwald, president of the Oregon Crime Victims Law Center, said some people worry that prosecutors — faced with a more difficult path to winning convictions — might simply elect not to pursue certain cases.

“We already have very low rates of prosecutions for sex crimes, and I can see in prosecutors’ minds why it might be too difficult to get a conviction, so they decide not to prosecute a case,” said Ms. Greenwald, who is herself a former prosecutor. “For crime victims, this is going to be more challenging and difficult.”