This will be a first-in-human pilot study assessing the feasibility and toxicity profile of NIH PyVST cellular product in subjects with PML. Subjects will be screened under the existing NIH Natural History study of PML (13-N-0017). Sequential enrollment will be spaced at least 28 days apart. An initial fixed dose PyVST infusion (target dose of 1 x 10^6 PyVST/kg (+/- 10%)) will be administered by intravenous (IV) infusion, followed by 2x10^6 PyVST/kg (+/-10%) up to 2 times to each subject if needed.