Although the nuclear lamina is considered to be the primary mechanical defense of the nucleus, lamins are part of an integrated network of lipids, proteins, and chromatin. Here, we isolate the contribution of chromatin to nuclear mechanics by employing fission yeast, which lack a nuclear lamina. We have combined a quantitative imaging platform capable of measuring 3D nuclear contours in vivo with an in vitro optical tweezers assay to probe the mechanical properties of S. pombe nuclei. In live cells, we find that association of chromatin with the inner nuclear membrane (INM) through integral membrane proteins is required for a normal mechanical response to microtubule (MT) forces. Increasing loss of integral INM proteins results in highly deformable nuclei specifically in response to exogenous MT forces. These nuclei also show a decreased capacity to recover from mechanical stress. Using optical tweezers, we find that nuclei lacking integral INM proteins are less stiff than wild type nuclei and have increased chromatin flow, particularly when force is applied at rates that recapitulate the kinetics of MT dynamics in vivo. Wild type mitotic nuclei, in which chromatin is globally released from the INM, are extremely soft and also display increased chromatin flow compared to interphase nuclei. Interestingly, decreasing the chromatin to nuclear volume ratio without altering the association of chromatin with the INM has only a slight effect on stiffness and does not alter chromatin flow. Together, these findings suggest that association of chromatin with the nuclear envelope underlies nuclear stiffness. Further, release of chromatin from the INM allows chromatin to flow into MT-dependent fluctuations of the nuclear envelope, leading to larger, longer-lasting nuclear deformations. Lastly, these results suggest that chromatin association with the lamina may contribute to the mechanical behavior of metazoan nuclei.