A Copiah County judge ruled against him in 2010, but the case is headed back to the state Supreme Court.
Chase's appeal is one of two death penalty cases scheduled for oral arguments during the court's November-December term.
Arguments in Chase's appeal are set for Dec. 10 in Jackson.
Chase was convicted and sentenced to death in 1990 for the killing of an elderly Copiah County vegetable salesman as his gagged wife watched helplessly.
Authorities said the body of Elmer Hart was found on his bedroom floor beside his wife.
Chase also has argued his lawyer failed to raise mental-handicap issues at his trial.
Hart, a 70-year-old who peddled vegetables, apparently had come home as his wife was being robbed by Chase and another man on Aug. 14, 1989, at the couple's rural home.
His wife had been doused with an ammonia-like substance and tied up, court records showed.
The Mississippi Supreme Court upheld Chase's sentence in 1994.
Chase has argued that a pretrial mental examination showed that he was mentally incapacitated.
Chase said he was examined by two doctors. But court regards show one doctor did not find Chase was mentally handicapped.
In a separate death row case, the Supreme Court will hear arguments from lawyers for Bobby Batiste on Dec. 5.
Batiste, a former Mississippi State University student, was sentenced to death in 2009 for killing his roommate.
Batiste was convicted of capital murder in Oktibbeha County in the March 2008 death of 28-year-old Andreas Galanis.
Prosecutors said Galanis died from a blow to the head after the two got into a fight at their off-campus apartment.
The fight began when Galanis discovered money missing from his checking account, prosecutors said. Batiste told police Galanis attacked him first, according to court records.
Lawyers for Batiste will ask the Supreme Court to consider his claim of self-defense.
Batiste said in statements to police that he used Galanis" debit card regularly and that Galanis knew about the transactions.
Other testimony from tellers at M&F Bank was that Galanis came to the bank the afternoon before he was killed and realized $4,507 was missing from his checking account.
The tellers testified Galanis told them he had never activated his debit card.
Bank officials testified that Galanis' bank statements show the card was activated at the branch ATM on Dec. 25, 2007 while Galanis was in Biloxi visiting his family.
Court records show Galanis told at least one teller that he suspected Batiste used the debit card without his permission.