Menopause is widely believed by biological anthropologists and life history theorists to have arisen early in human evolution. In this paper, I suggest that female reproductive senescence was the result of the escalating energetic cost of gestation, lactation and childcare that accompanied the continuing encephalization of early hominid offspring and the ensuing increase in infant altriciality, or helplessness, and the concomitant prolongation of juvenile dependence. Natural selection favored females who became prematurely infertile, as the escalating cost of raising each offspring led to maternal depletion and made it more profitable in terms of lifetime reproductive success to continue investing in existing offspring rather than attempting late pregnancies. Results of a mathematical model are presented which show that reproductive senescence can be advantageous even when maximum potential lifespan is only 50 years, if the premature cessation of reproduction allows females to moderately increase the survival and fertility of their existing subadult offspring. These findings suggest that menopause could have originated as much as 1.5 million years ago, and that if menopause is indeed such an old trait, it was more likely the result of selective pressure on females to invest more in their own children, as opposed to their grandchildren.