The six survivors will all eventually be tried
Rivas, 30, is accused of shooting dead a police officer on Christmas Eve 2000.
The gang broke out of a maximum security prison on 13 December 2000 and were on the run for six weeks before being recaptured in the town of Woodland Park in the neighbouring state of Colorado.
Five more gang members are expected to stand trial for murder - one of the escaped convicts committed suicide rather than surrender.
The court room was packed with colleagues of the dead officer, Aubrey Hawkins, who was found with 11 bullet wounds after investigating reports of a robbery at a shop in Irving, Texas.
The seven achieved nationwide notoriety during the manhunt - described as the biggest in the history of Texas.
A reward of $700,000 was offered for information leading to the capture of the entire gang.
Homemade knives
They broke out of Connally prison by using homemade knives to overpower guards.
They then stole the guards' clothing and bluffed their way to the rear gate.
Rivas is reported to have confessed to firing four shots at Hawkins but has refused to enter a plea in his trial.
In June, State District Judge Molly Francis entered a plea of not guilty on his behalf.
Defence lawyers have asked Judge Francis to throw out Rivas' confession, arguing that it was illegally obtained because he was denied prompt access to a state lawyer.
The prosecution has denied this claim.
If found guilty, Rivas and the five others could face the death penalty.