The high court has dealt with the case of the inmate, Thomas Miller-El, before. Last term, the justices ordered a federal appeals court to consider Miller-El's case and his claim.
The appeals court did, but ruled against him, taking several paragraphs in its opinion directly from the dissent of Justice Clarence Thomas in Miller-El's earlier case before the Supreme Court.
Miller-El was found guilty of murder in 1986 in Dallas. He was convicted of killing motel employee Doug Walker during a robbery.
But 10 of the 11 potential members of the jury who were black were stricken by peremptory challenges by the prosecution. It challenged only four of the 31 non-black potential jurors.
The justices should rule again in the case within a couple of months.