Final answer:
Chillingworth keeps Dimmesdale alive to enact a prolonged and psychological revenge for the adultery that Dimmesdale committed with Chillingworth's wife, believing this punishment to be more cruel than death.
Step-by-step explanation:
Chillingworth, a character in Nathaniel Hawthorne's novel The Scarlet Letter, keeps Reverend Arthur Dimmesdale alive because he seeks revenge. Chillingworth is the wronged husband of Hester Prynne, who commits adultery with Dimmesdale. Rather than seeking to kill Dimmesdale outright, Chillingworth wants him to live in agony and guilt. By keeping him alive, Chillingworth can continuously torment Dimmesdale, which he believes is a far more satisfying and cruel punishment than death.
The quoted lines suggest the idea that Chillingworth has the power to kill, but not the power to die, meaning he can exert power over Dimmesdale's life but cannot find peace in his own. Chillingworth's methods of revenge are psychological, causing Dimmesdale to suffer mentally and spiritually rather than hasten his physical death.