Neurons are challenged to maintain proteostasis in neuronal projections, particularly with the physiological stress at synapses to support intercellular communication underlying important functions such as memory and movement control. Proteostasis is maintained through regulated protein synthesis and degradation and chaperone-assisted protein folding. Using high-resolution fluorescent microscopy, we discovered that neurons localize a subset of chaperone mRNAs to their dendrites, particularly more proximal regions, and increase this asymmetric localization following proteotoxic stress through microtubule-based transport from the soma. The most abundant chaperone mRNA in dendrites encodes the constitutive heat shock protein 70, HSPA8. Proteotoxic stress in cultured neurons, induced by inhibiting proteasome activity or inducing oxidative stress, enhanced transport of Hspa8 mRNAs to dendrites and the percentage of mRNAs engaged in translation on mono and polyribosomes. Knocking down the ALS-related protein Fused in Sarcoma (FUS) and a dominant mutation in the heterogenous nuclear ribonucleoprotein A2/B1 (HNRNPA2B1) impaired stress-mediated localization of Hspa8 mRNA to dendrites in cultured murine motor neurons and human iPSC-derived neurons, respectively, revealing the importance of these RNA-binding proteins in maintaining proteostasis. These results reveal the increased dendritic localization and translation of the constitutive HSP70 Hspa8 mRNA as a crucial neuronal stress response to uphold proteostasis and prevent neurodegeneration.