Inclusion Criteria:  Male or female >= 18 years at the time of screening Able to provide written informed which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol Histologically or cytologically documented extensive stage-small cell lung cancer (ES-SCLC) (American Joint Committee on Cancer [AJCC] 8th edition stage IV or tumor/nodal volume that is too large to be encompassed in a tolerable radiation plan). Staging scans must include brain imaging with a computed tomography (CT) w/ contrast or magnetic resonance imaging (MRI) head and body imaging with a CT chest/abdomen/pelvis or a positron emission tomography (PET)/CT Patients with brain metastases are eligible provided they are asymptomatic, or treated and stable off steroids and anticonvulsants for at least 1 month before study entry Patients must be considered suitable to receive a platinum-based chemotherapy regimen as first-line treatment for ES-SCLC. Chemotherapy must contain either carboplatin or cisplatin in combination with etoposide Eastern Cooperative Oncology Group (ECOG) performance-status score of 0-1 at enrollment Life expectancy >= 12 weeks at enrollment Body weight > 30 kg No prior exposure to immune-mediated therapy including, but not limited to, other anti-cytotoxic T-lymphocyte-associated antigen-4, anti-programmed cell death-1, anti-programmed cell death ligand-1, and anti-programmed cell death ligand-2 antibodies, excluding therapeutic anticancer vaccines, NOT INCLUDING if patients are currently within the first 4 cycles of chemotherapy and durvalumab for THIS diagnosis of ES-SCLC within the past 4 months Hemoglobin >= 9.0 g/dL (within 3 prior months) Absolute neutrophil count >= 1.5 x 10^9/L (within 3 prior months) Platelet count >= 75 x 10^9/L (within 3 prior months) Serum bilirubin =< 1.5 x the upper limit of normal (ULN) (within 3 prior months). 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: Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2.5 x ULN; for patients with hepatic metastases, ALT and AST =< 5 x ULN (within 3 prior months) Measured or calculated creatinine clearance: of > 40 mL/min as determined by Cockcroft-Gault (using actual body weight) (within 3 prior months)  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:  Medical contraindication to platinum-etoposide Any anti-cancer therapies including chemotherapy, hormone therapy, or other immunotherapies in the 4 months prior to this diagnosis of ES-SCLC Concurrent enrolment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study Any history of radiotherapy to the chest History of allogenic organ transplantation Has a peripheral nervous system (PNS) of autoimmune nature, requiring systemic treatment (systemic steroids or immunosuppressive agents) or has a clinical symptomatology suggesting worsening of PNS  Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease [eg, colitis or Crohn's disease], diverticulitis with the exception of diverticulosis, systemic lupus erythematosus, sarcoidosis syndrome, or 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 (eg, following Hashimoto syndrome) stable on hormone replacement Any chronic skin condition that does not require systemic therapy Patients without active disease in the last 5 years may be included but only after consultation with the study physician Patients with celiac disease controlled by diet alone Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, interstitial lung disease, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, 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  History of another primary malignancy except for:  Malignancy treated with curative intent and with no known active disease >= 5 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 (eg, cervical cancer in situ) History of leptomeningeal carcinomatosis History of active primary immunodeficiency Active infection, including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis testing in line with local practice), hepatitis B virus (HBV) (known positive HBV surface antigen result), hepatitis C virus (HCV), or human immunodeficiency virus (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. 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 (eg, 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 (eg, CT scan premedication). Premedication with steroids for chemotherapy is acceptable Receipt of live, attenuated vaccine within 30 days prior to the first dose of durvalumab. Patients, if enrolled, should not receive live vaccine whilst receiving durvalumab and up to 30 days after the last 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