The poles of the mitotic spindle contain one old and one young centrosome. In asymmetric stem cell divisions, the age of centrosomes affects their behaviour and their probability to remain in the stem cell. In contrast, in symmetric divisions, old and young centrosomes are thought to behave equally. This hypothesis is, however, untested. In this study, we show in symmetrically dividing human cells that kinetochore-microtubules associated to old centrosomes are more stable than those associated to young centrosomes, and that this difference favours the accumulation of premature end-on attachments that delay the alignment of polar chromosomes at old centrosomes. This differential microtubule stability depends on cenexin, a protein enriched on old centrosomes. It persists throughout mitosis, biasing chromosome segregation in anaphase by causing daughter cells with old centrosomes to retain non-disjoint chromosomes 85% of the time. We conclude that centrosome age imposes via cenexin a functional asymmetry on all mitotic spindles.