The RNA binding protein TDP-43 forms intranuclear or cytoplasmic aggregates in age-related neurodegenerative diseases. In this study, we found that RNA binding-deficient TDP-43 (produced by neurodegeneration-causing mutations or posttranslational acetylation in its RNA recognition motifs) drove TDP-43 demixing into intranuclear liquid spherical shells with liquid cores. These droplets, which we named "anisosomes", have shells that exhibit birefringence, thus indicating liquid crystal formation. Guided by mathematical modeling, we identified the primary components of the liquid core to be HSP70 family chaperones, whose adenosine triphosphate (ATP)-dependent activity maintained the liquidity of shells and cores. In vivo proteasome inhibition within neurons, to mimic aging-related reduction of proteasome activity, induced TDP-43-containing anisosomes. These structures converted to aggregates when ATP levels were reduced. Thus, acetylation, HSP70, and proteasome activities regulate TDP-43 phase separation and conversion into a gel or solid phase.