At some point in the future – perhaps within the next few decades – it will be possible for foetuses to develop completely outside the womb. Ectogenesis, as this technology is called, raises substantial issues for the abortion debate. One such issue is that it will become possible for a woman to have an abortion, in the sense of having the foetus removed from her body, but for the foetus to be kept alive. We argue that while there is a right to an abortion, there are reasons to doubt that there is a right to the death of the foetus. Our strategy in this essay is to consider and reject three arguments in favour of this latter right. The first claims that women have a right not to be biological mothers, the second that women have a right to genetic privacy, and the third that a foetus is one's property. Furthermore, we argue that it follows from rejecting the third claim that genetic parents also lack a right to the destruction of cryopreserved embryos used for in vitro fertilization. The conclusion that a woman possesses no right to the death of the foetus builds upon the claims that other pro‐choice advocates, such as Judith Jarvis Thomson, have made.