Since he showed no signs of his deadly plans before he carried them out, we can easily assume he's capable of further murder, and can be held until he dies for public safety reasons. If Chapman had been going around saying "I'll be killing John Lennon Tuesday" then one might argue he's "gotten it out of his system". But because his current behaviour is similar enough to his pre-murdering behaviour, a reasonable person can reasonably assume he will kill again.

He will die in prison, there's no question of that. I wish he'd hurry up, though.