BOSTON — A man’s portrait has hung for years outside the chambers of the chief justice on Massachusetts’ highest court. The problem? No one knows who he is.

It’s a mystery that has stumped officials at the Supreme Judicial Court for more than a decade. Now they’re turning to the public for help in cracking the case of the unknown justice.

“I basically said, listen, if we have not been able to identify it, why don’t we set loose the public to see if they can put on their Sherlock Holmes’ hats and help us to track down who this elusive and mysterious justice is?” Chief Justice Ralph Gants, who has served on the court since 2009, said in an interview.

Officials say they believe the man may have sat on the bench sometime between 1780 and 1820.

Gants said they have essentially ruled out that the man was a chief justice but say he must have been an associate justice because they can’t imagine why else his portrait would be in the court, which traces its roots to 1692.

Even the artist remains unknown.

Clifford Allen, director of education and public programs for the court, said officials years ago attempted to identify all the portraits of the retired justices and put them on a CD. The anonymous painting was the only one they couldn’t figure out, he said.

Since then, research has turned up few clues.

Allen said he has tried matching the portrait with all of the justices who served during that era. He even ran the portrait through the Google program that matches a person’s likeness to a painting, he said.

The high court says the person that comes forward with reliable authentication of the portrait will be invited to the court to stand with Gants as he unveils a plaque bearing the mystery justice’s name. They’ll also get a guided tour of the John Adams Courthouse.