I consider the argument, thought to clinch the moral case for use of a human embryo solely as a means, that (i) only a human individual can be a person, (ii) because it can happen at any time before formation of the primitive streak that an embryo splits into monozygotic twins, no embryo in which the primitive streak has not formed is a human individual, and therefore (iii) no embryo in which the primitive streak has not formed is a person. I explore the following proffered arguments for (ii): (a) indivisibility is a necessary condition of individuality, (b) nonidentity of an embryo with successor twins impugns the embryo’s individuality, and (c) totipotency of an embryo’s constituents is inconsistent with the embryo’s being a human individual. These arguments are tested and found wanting; so too is an alternative to (a), the argument that indivisibility is intrinsic to personhood. Whereupon (ii) is unsustained. In search of ways to rehabilitate the nonindividuation argument, I canvass alternative metaphysical views and inquire further into biological individuality, but find that the argument cannot be saved. I conclude by analyzing where this leaves matters concerning the morality of embryo use.