JOSEPH Giarratano, who has spent 10 years on death row in Mecklenburg, Va., got the news Monday. The Supreme Court refused to hear an appeal in his case, setting the stage for his execution any time after a 30-day waiting period has elapsed. While it is still possible for his lawyers to file another habeas corpus petition in state court, they are not optimistic. Appellate courts in Virginia -- in stark contrast to the rest of the country -- seldom overturn convictions in capital cases. Mr. Giarratano's only chance of avoiding the electric chair probably lies now with Gov. L. Douglas Wilder.

After a half-day trial in 1979, Mr. Giarratano was convicted on two counts of murder and one of rape. These were truly terrible crimes. He had confessed to killing and assaulting a 15-year-old girl and murdering her mother. He entered a plea of not guilty by reason of insanity. Over the course of the past decade he was unsuccessful in his direct appeal and in habeas corpus proceedings in both state and federal courts.

You do not have to believe either that the convicted man was innocent or that his crimes were anything less than depraved to believe that Gov. Wilder should look carefully at this case, considering two things -- first, the overall appellate figures in Virginia and, second, the facts of this man's remarkable life since conviction.

According to the NAACP Legal Defense Fund and the Virginia Coalition on Jails and Prisons, more than 40 percent of all capital cases are reversed on direct appeal nationally. In Virginia, the figure is 7.25 percent. Across the country, 42.3 percent of those sentenced to death obtained relief in habeas corpus proceedings in state courts. In Virginia, not a single petitioner of 44 has been successful. Nationally, 25.7 percent of those sentenced to death obtain relief through federal habeas corpus proceedings in district court, and another 38.11 percent are successful on appeal. Federal district courts in Virginia have granted writs in only 11.7 percent of the cases; the U.S. Court of Appeals reversed half of these and granted not a single one itself.

The governor, of course, does not control the actions of state judges, let alone federal judges, but the state's own actions have contributed to these figures. Until recently, Virginia was one of only seven states that refused to provide lawyers for post-conviction appeals in capital cases. It is now the only state that makes no provision in capital cases for raising procedural questions on appeal that were not raised at trial. All Virginia's death penalty cases should be reviewed by the governor in light of this history.

As for Mr. Giarratano himself, he has, by all accounts, changed, become an exemplary and productive inmate. He is more than a jailhouse lawyer, having prepared the papers in a number of successful suits and at least one landmark case involving right to counsel. He has become a spokesman for death-row inmates, has published essays and newspaper articles, collaborated with law professors and been interviewed on national television and by the foreign press. His reform and his accomplishments -- not his celebrity -- merit the governor's review at least as to whether they justify a more merciful sentence.