In "Hamlet," why doesn't Hamlet kill Claudius in the "prayer scene" of Act 3, Scene 3?
As soon as Polonius exits the scene, Claudius laments about his inability to pray and the guilt he is experiencing after murdering his brother. As Claudius proceeds to contemplate his sin and wonder whether or not he can ask God for forgiveness, he kneels down as Hamlet silently enters the room. Knowing that he has a perfect opportunity to kill King Claudius, Hamlet draws his sword. However, Hamlet hesitates and says,
"And so he goes to heaven. And so am I revenged.—That would be scanned. A villain kills my father, and, for that, I, his sole son, do this same villain send To heaven. Oh, this is hire and salary, not revenge" (Shakespeare, 3.3.75-80).
Hamlet refuses to kill Claudius while praying, because he believes that Claudius's spirit will go to heaven since he is in the process of asking God for forgiveness. Hamlet knows that his father never had a chance to repent for his numerous sins before Claudius murdered him and does not think that sending Claudius's soul to heaven would be adequate revenge. Essentially, killing Claudius is not enough for Hamlet, who wishes to send Claudius's soul to hell for eternity. Hamlet hopes to kill his uncle while he is excessively drinking alcohol, gambling, or "in th' incestuous pleasure of his bed" in order to ensure that his soul will suffer in hell.
Although Hamlet initially believes he has an ideal opportunity to kill Claudius in this scene ("Now might I do it"), he puts up his sword when he realizes that if he kills Claudius while the king is praying, he will send Claudius to heaven because the king will have confessed his sins. His goal is for Claudius to suffer the same fate Claudius created for Hamlet's father, who died without benefit of confession and therefore is "confined to fires" during the day until his sins are burned away. Hamlet decides that he will wait until he catches Claudius in some sinful activity and then kill him.
The irony, of course, is that Claudius is unable to pray because he is unwilling to relinquish what he gained by killing his brother. Though he regrets that act ("my offense is rank!"), he cannot give up what he gained---the crown and Gertrude---if he confesses his sin. He is kneeling, but he is not praying. If Hamlet had killed him at this point, he would have achieved his goal.
I discuss this aspect of the play in free, online lessons on Hamlet here at eNotes. Please click the link below for summary and analysis, and as you continue on with the tragedy, you may wish to check in on other lessons and discussion questions.