03/22/2012 05:02 pm ET

Nathan Dunlap, Convicted In 1996 For Chuck E. Cheese Murders, Trying To Overturn Death Sentence

One of the three men on Colorado's death row asked a federal court Tuesday to overturn his death sentence citing mental illness.

Nathan Dunlap, 37, was sentenced to death after killing four people at a Chuck E. Cheese restaurant 19 years ago. Three of his victims were teenagers and the fourth was a mother of two. At the time of the murders, Dunlap himself was 19 and he has consequently spent about half of his life awaiting his own execution on death row.

"Nathan Dunlap is running out of time. This is his last, best chance," defense attorney David Lane--who isn't representing Dunlap--told the Associated Press. "If he loses here, his odds of being executed skyrocket."

Dunlap's attorneys argued that he is mentally ill and that his trial lawyers did not fairly represent him.

After the jury delivered four guilty verdicts, Dunlap's attorney, Forrest Lewis, reportedly told jurors:

If you choose to kill my client on the facts of this case, I will respect that. Nathan Dunlap chose to kill. He should be held accountable. He has been held accountable. But you have a choice now, too. Choose life. Not violence. Not killing. But life.

The last person executed in Colorado was Gary Davis, and that was 15 years ago. Davis was also the first Colorado inmate to be executed by lethal injection, rather than the gas chamber.

It could take months for the judges on the 10th Circuit to issue a ruling, and 9News reports that if Dunlap wins his hearing, his case will return to the state court which may decide to give him life in prison.