Question: What is the Objectivist opinion on capital punishment? Is morality a good argument against capital punishment?
Answer: Ayn Rand argued that those who mete out death to others certainly deserve it back as a matter of justice (assuming that we are speaking of someone who initiated force). In this sense, there is no moral argument against the death penalty. People deserve respect for their rights, including their right to life, and are potential trading partners for us only so long and insofar as they are rational beings. But people who show a character that has basic disregard for human life (as do serial killers, for example, or mass-murdering terrorists) are not in that class, and by initiating force against others and causing death by intention, they open themselves up in justice to any proportional punishment. Death is in many ways too small a price for some crimes, morally speaking.
However, Rand was rightly concerned that as a matter of practical epistemology, it is difficult to know with certainty whether an accused person has truly committed a capital crime. Since a death penalty, once enforced, can never be taken back, she thought in practice it should only be applied in rare cases.
However, this is an issue that is in debate in Objectivist circles. TAS as such has no position on it. Ultimately, this a matter that depends a great deal on the legal and scientific context: what we can justly prove, and what we can know about the past.