How does a governor make such a decision, and what kind of things does he take into consideration?
WRAL's Amanda Lamb went to the state Capitol to find out.
Unlike a court of law, the governor can consider anything when it comes to deciding whether or not to stop an execution. He is granted that power under the state constitution.
In the Hill case, he will review court files and talk to lawyers, but he also can take into consideration the inmate's prison record and concerns of the inmate's family and friends.
By law, at this stage of the game, Hunt is the only person who can prevent Hill's execution.
Six executions have taken place at Central Prison since Hunt was elected. He has never granted clemency for a death row inmate.
"There is a very good argument that clemency is the appropriate moral and humane response," said Pat McCoy, president of People of Faith.
Some protesters believe this case should be an exception. Zane Hill was convicted of shooting his 29-year-old son to death during a drunken rage in 1990 in Buncombe county. His family and friends are lobbying to stop the execution.
"The family has clearly stated they believe it is in their best interest for his life to be spared," said McCoy.
The governor can deny the request for clemency all together, or change the penalty to life in prison.
"That gives him virtually unlimited authority in that regard, and so basically the governor can exercise that power as he deems appropriate," said North Carolina Court of Appeals Judge Mark Martin.
Before he was on the bench, Martin was legal counsel to former governor Jim Martin. In 1991 Jim Martin commuted the sentence of a person on death row. Judge Mark Martin says this is rare.
"But I would add that governors are reluctant to intervene when the judicial system has already spoken," said Mark Martin.
Tomorrow the governor will meet with the North Carolina Council of Churches which opposes the execution. He will also be talking to lawyers and relatives and friends of Hill.
It could be as late as Thursday before he makes a decision.