The nuclear lamina is thought to be the primary mechanical defence of the nucleus. However, the lamina is integrated within a network of lipids, proteins and chromatin; the interdependence of this network poses a challenge to defining the individual mechanical contributions of these components. Here, we isolate the role of chromatin in nuclear mechanics by using a system lacking lamins. Using novel imaging analyses, we observe that untethering chromatin from the inner nuclear membrane results in highly deformable nuclei in vivo, particularly in response to cytoskeletal forces. Using optical tweezers, we find that isolated nuclei lacking inner nuclear membrane tethers are less stiff than wild-type nuclei and exhibit increased chromatin flow, particularly in frequency ranges that recapitulate the kinetics of cytoskeletal dynamics. We suggest that modulating chromatin flow can define both transient and long-lived changes in nuclear shape that are biologically important and may be altered in disease.