JACKSON, Miss, Oct. 9— Three years ago, in an attempt to heal old wounds, officials reopened one of the most searing cases from the Civil Rights era: the 1963 assassination of the civil rights leader Medgar Evers.

On Thursday, the Mississippi Supreme Court hears arguments that could rip those wounds open again.

The question is whether a new murder trial of his accused assassin, Byron De La Beckwith, a 71-year-old white supremacist, should go forward or whether the murder charges, filed in 1990, should be dismissed. The case also raises a broader issue: Is the legacy of the South's white-supremacist past, in which white law officers and all-white juries routinely left murders of blacks unpunished, a subject for the legal system or history books?

Defense lawyers say the passage of time makes a fair trial impossible and some legal scholars say the changes in the South make a trial unnecessary. Beyond that, the Mississippi Supreme Court's unusual decision to take up the defense's contention that the right to a speedy trial has been violated -- even before the trial begins -- has led some people to speculate that the justices will dismiss the case. Blacks Cite Symbolic Justice

"It's just too far away from the facts of the case to have a fair trial," said Bruce Fein, a conservative legal scholar in Washington. "I can think of some special circumstances, where you had to make a moral statement that hadn't been made for many years. But now the law and the community sentiment is favorable to minorities."

But many blacks say Mr. Beckwith can get a fair trial. They say a prosecution would serve the symbolic purpose of providing justice where justice was so often denied and the practical purpose of showing that wrongs from the civil rights era can still be righted.

"It would close a chapter, and allow us to go forward knowing justice was done," said Daniel T. Williams, archivist at Tuskegee University, which has compiled records of 4,709 racially motivated murders, most of them lynchings of blacks in the South, committed between 1886 and 1966. In almost all of them, the killers went free.

Reopening the Evers case has also renewed interest in some of the other unsolved civil rights slayings.

The two previous trials of Mr. Beckwith on charges of killing Mr. Evers ended in mistrials in 1964 when all-white juries could not agree on a verdict. Five years later, the charges against him were dropped. Mr. Beckwith, who is in jail, has steadfastly maintained his innocence.

Prosecutors reopened the case in late 1989 when state documents were unsealed disclosing that a now-defunct state agency, the Mississippi Sovereignty Commission, which sought to preserve segregation, secretly aided his defense in his second trial by screening potential jurors. A new indictment was handed up, and a new trial date was set for Sept. 21.

But, in an unusual step in August, the Mississippi Supreme Court halted the retrial to hear defense arguments that a new trial would violate Mr. Beckwith's right to a speedy trial, would constitute double jeopardy and would violate his right to a fair trial.

Judge Breland Hilburn of Hinds County Circuit Court turned down the motion before the trial was transferred to DeSoto County. Of the Supreme Court's action, Michael Holleman, a Gulfport criminal lawyer, said, "I don't think it necessarily suggests an outcome, but it's very unusual for the court to take up the speedy-trial question before the trial begins."

Prosecutors contend that Mr. Beckwith's defense remains unharmed by the passage of time. They also cite legal precedent saying that when charges against Mr. Beckwith were dismissed in 1969, the issues revolving around the Constitution's guarantee of a speedy trial became moot because he was no longer charged with a crime.

"If the Mississippi Supreme Court does indeed dismiss this case, it will be a travesty for Medgar's survivors and for those who worked side by side with him and paid very high prices for freedom," said his widow, Myrlie Evers. Evers Shot in Back

The Evers case dates to June 12, 1963, when Mr. Evers, 37, Mississippi field secretary for the National Association for the Advancement of Colored People, was fatally shot in the back outside his Jackson home. Mr. Beckwith was arrested 11 days later. A rifle with his fingerprints was found near the scene of the crime and witnesses linked him to the murder scene.

Mr. Beckwith's defense centered on two police officers in his hometown of Greenwood, about a two-hour drive from Jackson, who said they saw him there less than an hour after the murder was committed. Prosecutors have collected new evidence, including several witnesses who say Mr. Beckwith bragged to them about committing the murder. The two police officers stand by their original testimony.

The defense argues that both the five-year gap between the 1964 trials and the dismissal of charges and the 29-year gap between the crime and the new indictment violate Mr. Beckwith's right to a speedy trial. They say his declining health, the deaths of his original lawyers and numerous witnesses, and the disappearance of files and evidence make a fair trial impossible.