Chromosomal instability leading to aneuploidy is pervasive in early human embryos^{, –} and is considered as a major cause of infertility and pregnancy wastage^,. Here we provide several lines of evidence that blastocysts containing aneuploid cells are worthy of in vitro fertilization transfer. First, we show clinically that aneuploid embryos can lead to healthy births, suggesting the presence of an in vivo mechanism to eliminate aneuploidy. Second, early development and cell specification modelled in micropatterned human ‘gastruloids’ grown in confined geometry show that aneuploid cells are depleted from embryonic germ layers, but not from extraembryonic tissue, by apoptosis in a bone morphogenetic protein 4 (BMP4)-dependent manner. Third, a small percentage of euploid cells rescues embryonic tissue in mosaic gastruloids when mixed with aneuploid cells. Finally, single-cell RNA-sequencing analysis of early human embryos revealed a decline of aneuploidy beginning on day 3. Our findings challenge two current dogmas: that a single trophectoderm biopsy at blastocyst stage to perform prenatal genetic testing can accurately determine the chromosomal make-up of a human embryo, and that aneuploid embryos should be withheld from embryo transfer in association with in vitro fertilization.