Centrosomes are vital mechanical hubs in cells. They nucleate microtubules and sustain load-bearing attachments to these microtubules during assembly of the mitotic spindle, segregation of chromosomes, and positioning of the nucleus. During these processes microtubule-centrosome attachments sustain considerable forces, and the number of attachments is regulated in correlation with the forces they sustain. However, their mechanical strength has never been directly measured, and the possibility that mechanical force may regulate their function has not been explored. To uncover how centrosomes sustain and regulate microtubule attachments, we purified centrosomes from budding yeast and used single-molecule laser trapping to manipulate single microtubules attached to centrosomes in vitro. Yeast centrosomes are ideal for biophysical studies, since their composition and structure are known more completely than in any other organism. Single-molecule laser trapping experiments, in which the force on individual microtubule-centrosome attachments was increased at a rate of 5 pN/s, revealed that individual centrosome-microtubule attachments sustain tensile loads of approximately 40 pN. This force is four times greater than the forces thought to be generated at a single kinetochore-microtubule attachment during mitosis. This result implies that a single microtubule-centrosome attachment is sufficient to support the segregation of an individual chromosome in yeast. We also found that mutations in the Spc110 protein, which is involved in binding microtubules to centrosomes, significantly (p = 0.004) weakened the strength of microtubule attachments compared to wild-type centrosomes. This reduced strength might explain why cells with this mutation are arrested by the Mad1 spindle-assembly checkpoint of mitosis, which implies that the mitotic spindle in these cells is unable to support enough tension to silence kinetochore-generated wait signals. Further studies aim to reveal how specific protein components, molecular interfaces, and phosphorylation sites are involved in sustaining, sensing, and regulating the forces transmitted by microtubules.