Chikungunya virus (CHIKV), a mosquito-borne human pathogen, causes a disabling disease characterized by severe joint pain that can persist for weeks, months or even years in patients. The non-structural protein 3 (nsP3) plays essential roles during acute infection, but little is known about the function of nsP3 during chronic disease. Here, we used sub-diffraction multi-color microscopy for a spatial and temporal analysis of CHIKV nsP3 within human cells that persistently replicate viral RNA. Round cytoplasmic granules of various sizes (i) contained nsP3 and G3BP Stress Granule Assembly factor; (ii) were next to double-stranded RNA foci, and nsP1-positive structures; and (iii) made contact with markers of the cytoskeleton and cellular structures, such as early endosomes and nucleopores. Analysis of protein turnover and mobility by live-cell microscopy revealed that granules could persist for hours to days, can accumulate newly synthesized protein, and move differently through the cytoplasm. Granules also had a static internal architecture and were stable in cell lysates. Whereas cells with active replication and stable nsP3-granules did not respond to oxidative stress, refractory cells that had cleared the non-cytotoxic replicon could. In summary, nsP3 can form uniquely stable granular structures that persist long-term within the host cell. This continued presence of viral and cellular protein-complexes has implications for the study of the pathogenic consequences of lingering CHIKV infection and the development of strategies to mitigate the burden of chronic musculoskeletal disease brought about by a medically important arthropod-borne virus (arbovirus).