Caryl Chessman did not kill any one. He was known as the red light bandit. He would stake out lovers lanes and assault people as they were parked. I believe the controversy in the Chessman case is that he was not convicted of killing anyone.
The controversy in Chessman's case was fanned by the fact that he wrote an autobiography, "Cell 2455, Death Row". It became a best seller. He was quite articulate, and sounded like someone who might be rehabilitated.
He wasn't accused of killing anyone, but as someone said, preyed on lover's lane couples. Evidently the Red Light Bandit made his women victims commit oral sex, and believe it or not in this era of Bill Clintoon, a lot of people were sincerely shocked and sickened by this.
As I recall, he turned down a plea which would have spared his life, and then made the mistake of representing himself at his trial. He himself admitted that he had a fool for a client.
He was on California's death row longer than anyone else had ever been (14 years +/-).
He was executed at San Quentin in 1960, and that stirred up a nationwide controversy about the death penalty. I believe it wasn't too long afterwards that the Supremes ruled against the death penalty, and that was probably fueled by Chessman's case.