If, as a number of writers have predicted, the computers of the future will possess intelligence and capacities that exceed our own then it seems as though they will be worthy of a moral respect at least equal to, and perhaps greater than, human beings. In this paper I propose a test to determine when we have reached that point. Inspired by Alan Turing’s (1950) original “Turing test”, which argued that we would be justified in conceding that machines could think if they could fill the role of a person in a conversation, I propose a test for when computers have achieved moral standing by asking when a computer might take the place of a human being in a moral dilemma, such as a “triage” situation in which a choice must be made as to which of two human lives to save. We will know that machines have achieved moral standing comparable to a human when the replacement of one of these people with an artificial intelligence leaves the character of the dilemma intact. That is, when we might sometimes judge that it is reasonable to preserve the continuing existence of a machine over the life of a human being. This is the “Turing Triage Test”. I argue that if personhood is understood as a matter of possessing a set of important cognitive capacities then it seems likely that future AIs will be able to pass this test. However this conclusion serves as a reductio of this account of the nature of persons. I set out an alternative account of the nature of persons, which places the concept of a person at the centre of an interdependent network of moral and affective responses, such as remorse, grief and sympathy. I argue that according to this second, superior, account of the nature of persons, machines will be unable to pass the Turing Triage Test until they possess bodies and faces with expressive capacities akin to those of the human form.