Born in Houston, Texas, Parker received a Bachelor of Arts degree from Rice University in 1959 and a Bachelor of Laws from the University of Texas School of Law in 1962.

He served as Chief Judge from 2000 to 2003, assuming senior status on September 1, 2003.

[1] He was involved in the Wen Ho Lee nuclear espionage case.

He formally denounced the government for abuse of power in its prosecution of the case.

[2][3][4] Later, President Bill Clinton remarked that he had been "troubled" by the way Dr. Lee was treated.