Most animal cells contain a centrosome, which comprises a pair of centrioles surrounded by an ordered pericentriolar matrix (PCM). Although the role of this organelle in organizing the mitotic spindle poles is well established, its precise contribution to cell division and cell survival remains a subject of debate. By genetically ablating key components of centriole biogenesis in chicken DT40 B cells, we generated multiple cell lines that lack centrioles. PCM components accumulated in acentriolar microtubule (MT)-organizing centers but failed to adopt a higher-order structure, as shown by three-dimensional structured illumination microscopy. Cells without centrioles exhibited both a delay in bipolar spindle assembly and a high rate of chromosomal instability. Collectively, our results expose a vital role for centrosomes in establishing a mitotic spindle geometry that facilitates correct kinetochore–MT attachments. We propose that centrosomes are essential in organisms in which rapid segregation of a large number of chromosomes needs to be attained with fidelity.