Gilley is from Houston. He is accused of killing his wife. She was pregnant when she died.

Gilley was out on a $1 million bond. His trial was set to start soon. Weeks before the trial, he ran. He cut off his ankle monitor. The court made him wear it. Then he flew to Italy.

Prosecutors say he used a fake name. They say he used fake travel papers. He also talked with a woman outside Texas. They talked about a plan. The plan was to run and get a new identity.

Italian police caught Gilley. He has been locked up in Italy since early May.

Now Italy and the U.S. are in a fight. The fight is over Gilley. Can he be sent back to Texas? This kind of fight is called extradition.

A court in Turin, Italy is handling it. It is called the Court of Appeal. That court asked the U.S. for a promise. Italian judges want proof. They want proof Gilley will not get the death penalty. This is for if he goes back and is found guilty. A hearing on this is set for next month.

Harris County District Attorney Sean Teare answered. He filed a notice with the court. The notice says his office will not seek the death penalty against Gilley.

"The State of Texas officially notifies the Court that it will not seek the death penalty against the defendant," Teare wrote.

Teare said this cannot be undone. He called it "irrevocably binding." That means locked in for good. It binds the Harris County District Attorney's Office. He said it is binding "in perpetuity." In perpetuity means forever. No future Harris County DA can change it.

Teare's filing says Gilley keeps telling the Italian court something false. Teare says Gilley "falsely insists" he still faces the death penalty.

"It is our hope that this notice will put an end to the defendant's charade so that he can be tried by a jury or judge in the United States and the victims receive the justice they deserve," Teare said.

Gilley still faces a capital murder charge in Texas. That is the most serious murder charge in the state. He is accused of killing his pregnant wife.

The extradition hearing in Turin is set for next month.

Everyone is presumed innocent until proved otherwise.