The purpose of the clinical trial is to study the therapeutic efficacy and safety of Stemchymal® infusions for polyglutamine spinocerebellar ataxia treatment by a randomized, double-blind, placebo-controlled study design. Eligible subjects will receive Stemchymal® through intravenous infusion.

Inclusion Criteria:

1. Subjects are with genotypically confirmed spinocerebellar ataxia type 2 or spinocerebellar ataxia type 3.
2. Subjects' baseline SARA score are in the range of 8 to15.
3. Subjects are between 20 and 70 years of age.
4. Subjects who had signed informed consent.

Exclusion Criteria:

1. Subjects had been enrolled in any kind of cell therapy within six months prior to screening visit.
2. Females with a positive pregnancy test result.
3. Subjects who had had severe vital organ disease as diagnosed, including but not limited to cardiac (ex. heart failure), liver (ex. acute hepatic failure or chronic liver cirrhosis), lung (ex. respiratory failure) and renal (ex. hemodialysis or peritoneal dialysis) insufficiency, within six months prior to screening visit.
4. Subjects with immunological disorders (ex. Systemic lupus erythematosus), within six months prior to screening visit.
5. Subjects with other neurological disorders (ex. Alzheimer's disease), within six months prior to screening visit.
6. Subjects who had received chemotherapy/radiotherapy within five years prior to screening visit.
7. Subjects with any history of malignancy tumors.
8. Subjects with a history of hypersensitivity/allergy to penicillin.
9. Subjects with dementia or other psychiatric illnesses, including but not limited to disabling depression, bipolar disorder, and schizophrenia.
10. Subjects with Beck Depression Inventory Second Edition (BDI-II) score over 20 points.
11. Subjects with unstable illnesses or contraindication for this clinical trial according to PI's judgment.