Study of ADI-PEG 20 or Placebo Plus Gem and Doc in Previously Treated Subjects With Leiomyosarcoma (ARGSARC)

Inclusion Criteria: * A subject will be eligible for study participation if he/she meets the following criteria: 1. Histologically or cytologically confirmed, grade 2 or 3, LMS STS that would be standardly treated with Gem or GemDoc. 2. Determination of LMS subtype: uterine or non-uterine. 3. Measurable disease per RECIST 1.1 (Appendix A), defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. 4. Previous treatment with up to 2 systemic regimens, including at least 1 systemic regimen containing doxorubicin. 5. Treatment \> one year ago in the adjuvant/neoadjuvant setting with Gem or Doc is allowed. 6. Age \>18 years. 7. Eastern Cooperative Oncology Group (ECOG) performance status of \< 1 at enrollment (Appendix B). 8. Leukocytes ≥ 3,000/mcL. 9. Absolute neutrophil count ≥ 1,500/mcL. 10. Platelets ≥ 100,000/mcL. 11. Hemoglobin ≥ 8.0 g/dL 12. Total bilirubin ≤ 2 x ULN. (≤ 3 x ULN for potential subjects with Gilbert's Disease) 13. AST(SGOT)/ALT(SGPT) ≤ 3 x ULN (or ≤ 5 x ULN if liver metastases are present) 14. Creatinine clearance ≥ 60 mL/min (by Cockcroft-Gault equation). 15. Serum uric acid ≤ 8 mg/dL (with or without medication control). 16. QTc interval range from 350 to 450 ms for adult men and from 360 to 460 ms for adult women. 17. Subjects and their partners must be asked to use appropriate contraception. They must agree to use 2 forms of contraception or agree to refrain from intercourse for the duration of the study and for 35 days after the last dose of ADI-PEG 20 or for at least 3 months (male subjects) or 6 months (female subjects) after treatment with gemcitabine, whichever is the longer duration. 18. Ability to understand and willingness to sign the informed consent form. 19. No concurrent investigational drug studies are allowed. Exclusion Criteria: * A subject will not be eligible for study participation if he/she meets any of the exclusion criteria: 1. Subjects with history of another primary cancer, including co-existent second malignancy, with the exception of: a) curatively resected non-melanoma skin cancer; b) curatively treated cervical carcinoma in situ; or c) other primary solid tumor with no known active disease present in the opinion of the Investigator will not affect subject outcome in the setting of current diagnosis. 2. Currently receiving chemotherapy, immunotherapy, interferon, radiation therapy or other investigational agents. Note: Chemotherapy agent washout period is 5 half-lives prior to randomization. Radiation washout period is 7 days prior to randomization. 3. Prior treatment with ADI-PEG 20, Gem or Doc. Patients treated \> one year ago in the adjuvant/neoadjuvant setting with Gem or Doc are allowed to be enrolled. 4. Prior pelvic radiation. 5. Known brain metastases. Such patients must be excluded from this trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. 6. History of allergic reactions attributed to compounds of similar chemical or biologic composition to ADI-PEG 20, Gem, Doc, polysorbate 80, pegylated compounds, or other agents used in this study. 7. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 8. History of seizure disorder not related to underlying cancer. 9. Grade 2 or higher neuropathy. 10. Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry. 11. Known HIV-positivity. Because of the potential for pharmacokinetic interactions of antiretroviral therapy with the study treatment. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. 12. Currently receiving other immunosuppressive agents. 13. Subjects under guardianship, curatorship, under legal protection or deprived of liberty by an administrative or judicial decision