Inclusion Criteria:  Adults ≥ 18 years old Written informed consent from subject or from Health Care Proxy prior to performing any protocol-related procedures, including screening evaluations. Pathological diagnosis of SCLC from biopsy (core biopsy or fine needle aspiration); mixed-histology (NSCLC and SCLC) allowed ES-SCLC (American Joint Committee on Cancer, 8th edition, stage IV [T any, N any, M1a or M1b], or T3-4 due to multiple lung nodules that are too extensive or tumor or nodal volume that is too large to be encompassed in a tolerable radiation plan) Brain metastases allowed, but must be asymptomatic without the need for systemic steroids at doses more than 10 mg/day of prednisone or its equivalent, or treated with Whole Brain Radiation Therapy (WBRT) or Stereotactic Radiosurgery (SRS) Body weight > 30kg ECOG Performance Status (PS) 0-1 at enrollment. ECOG PS 2 allowed if PS decline considered by treating study investigator to be secondary to SCLC At least 1 lesion that can be accurately measured at baseline as ≥10 mm in the longest diameter (except lymph nodes, which must have a short axis ≥15 mm) with CT, PET-CT, or MRI and that is suitable for accurate repeated measurements as per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 guidelines. No prior exposure to IO therapy including, but not limited to, anti-CTLA-4, anti-PD-1, antiPD-L1, and anti-PD-L2 antibodies No prior radiation therapy in the past 3 years prior to study enrollment. Radiation treatment of brain metastases from small cell lung cancer will be permitted, as per inclusion criteria 5 above. Other specific radiotherapy treatments occurring within the past 3 years, such as electron beam therapy for skin cancers, pterygium irradiation with Sr-90 or SRS for non-malignant disease, or prior I-131 for hyperthyroidism, may not be an absolute contraindication, and will be considered on a case by case basis. Life expectancy of at least 12 weeks from the start of therapy  Adequate baseline organ functions as defined below  Hemoglobin ≥8.0 g/dL. Absolute neutrophil count ≥1.5 × 103/uL (use of granulocyte colony-stimulating factor is not permitted at screening). Platelet count ≥75 × 103/uL. Serum bilirubin ≤1.5 × the ULN. This will not apply to patients with confirmed Gilbert's syndrome, who will be allowed in consultation with their physician. In patients without hepatic metastasis: ALT and AST ≤2.5 × ULN; for patients with hepatic metastases, ALT and AST ≤5 × ULN. Measured or calculated creatinine clearance: >60 mL/min for patients on cisplatin and >45 mL/min for patients on carboplatin, as determined by Cockcroft-Gault (using actual body weight). Males: Creatinine clearance (mL/min) = [Weight (kg) × (140 - Age)]/[72 × serum creatinine (mg/dL)] Females: Creatinine clearance (mL/min) = [Weight (kg) × (140 - Age)]/ [72 × serum creatinine (mg/dL)] × 0.85  Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrhoeic for 12 months without an alternative medical cause. The following age-specific requirements apply:  Women <50 years of age would be considered post-menopausal if they have been amenorrhoeic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). Women ≥50 years of age would be considered post-menopausal if they have been amenorrhoeic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses >1 year ago, had chemotherapy-induced menopause with last menses >1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy, or hysterectomy).  Exclusion Criteria:  Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria  Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after consultation with the Study Physician. Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the Study Physician. Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or the follow-up period of an interventional study. Participation in another clinical study with a therapeutic investigational product during the last 4 weeks. Contraindications to platinum-based chemotherapy Contraindications to radiation therapy Prior radiation therapy to same site as proposed SBRT site Cannot tolerate radiation treatment position or immobilization Any concurrent chemotherapy, investigational product, biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable, as is use of bisphosphonate or RANKL inhibitor therapy for prevention of skeletal-related events from bone metastases.  History of another primary malignancy except for:  Malignancy treated with curative intent and with no known active disease ≥3 years before the first dose of the investigational product and of low potential risk for recurrence. Adequately treated nonmelanoma skin cancer or lentigo maligna without evidence of disease. Adequately treated carcinoma in situ without evidence of disease (e.g., cervical cancer in situ). History Limited-Stage SCLC treated with concurrent chemo-radiation History of allogenic organ transplantation. Major surgical procedure (as defined by the investigator) within 28 days prior to Cycle 1 Day1 of systemic therapy and SBRT. Local surgery of isolated lesions for palliative intent is acceptable. Paraneoplastic syndrome of autoimmune nature, requiring systemic treatment (systemic steroids or immunosuppressive agents)  Documented, active, and uncontrolled autoimmune or inflammatory disorders (including inflammatory bowel disease, diverticulitis with the exception of diverticulosis, systemic lupus erythematosus, sarcoidosis syndrome, Wegener syndrome (granulomatosis with polyangiitis), Graves' disease, rheumatoid arthritis, hypophysitis, and uveitis, etc.). The following are exceptions to this criterion:  Patients with vitiligo or alopecia. Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement Any chronic skin condition that does not require systemic therapy. Patients with celiac disease controlled by diet alone. Patients without active disease in the last 5 years may be included but only after consultation with the medical monitor and with appropriate subspecialty consultation (e.g. with endocrinology, gastroenterology, rheumatology, etc.) Patients whose autoimmune or inflammatory disorder is controlled with medication may be included but only after consultation with the medical monitor and with appropriate subspecialty consultation (e.g. with endocrinology, gastroenterology, rheumatology, etc.) Uncontrolled intercurrent illness, including but not limited to, uncontrolled ongoing or active infection, interstitial lung disease, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring adverse events, or compromise the ability of the patient to give written informed consent. Active infection, including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis testing in line with local practice), HBV (known positive HBV surface antigen result), HCV, or HIV (positive HIV 1/2 antibodies). Patients with a past or resolved HBV infection (defined as the presence of HBV core antibody and absence of HBV surface antigen) are eligible, as are patients with HBV infection controlled by antiviral medication (defined as undetectable viral load). Patients positive for HCV antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid.  Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab. The following are exceptions to this criterion:  Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra-articular injection). Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication). Premedication with steroids for chemotherapy is acceptable. History of active primary immunodeficiency. Receipt of live, attenuated vaccine within 30 days prior to the first dose of durvalumab Female patients who are pregnant or breast-feeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab monotherapy. Known allergy or hypersensitivity to durvalumab, etoposide, carboplatin, cisplatin, or any of their excipients.