Inclusion Criteria:

* PRIOR TO STEP 1 REGISTRATION
* Histologic proof or unequivocal cytologic proof (fine needle aspiration, biopsy or two positive sputa) of SCLC within 250 days prior to Step 1 registration

* High-grade neuroendocrine carcinoma or combined SCLC and NSCLC is permitted.
* Patients must have received chemotherapy and be registered to Step 1 registration no earlier than 7 days and no later than 56 days after completing chemotherapy. Note:

* Post-chemotherapy restaging imaging must be completed no more than 56 days prior to Step 1 registration.
* For patients with extensive-stage small cell lung cancer who are being considered for consolidative thoracic radiotherapy after chemotherapy, concomitant administration of consolidative thoracic radiotherapy and protocol-specified prophylactic cranial irradiation with or without hippocampal avoidance is permitted.
* Patients must have a gadolinium contrast-enhanced three-dimensional (3D), spoiled gradient (SPGR), magnetization-prepared rapid gradient echo (MP-RAGE), or turbo field echo (TFE) MRI scan (see section 11.3 regarding axial T2/FLAIR sequence). To yield acceptable image quality, the gadolinium contrast-enhanced three-dimensional SPGR, MP-RAGE or TFE axial MRI scan must use the smallest possible axial slice thickness not exceeding 1.5 mm. Sites may contact the Imaging Co-Chairs for further information or assistance if needed.

* This MRI must be obtained within 56 days prior to Step 1 registration. Note: The MRI study is mandatory irrespective of randomization to the experimental or control arm of this study.
* Prior to chemotherapy +/- thoracic radiotherapy, patients must be defined as limited-stage or extensive-stage SCLC after clinical staging evaluation involving the following:

1. History/physical examination;
2. CT of the chest and abdomen with contrast (does not have to be done if the patient has had a PET/CT scan prior to initiating chemotherapy or thoracic radiotherapy);
3. MRI of the brain with contrast or diagnostic head CT with contrast;
4. For patients without evidence of extensive-stage SCLC on chest and abdomen CT and brain MRI or head CT, a PET/CT or bone scan is required to confirm limited-stage SCLC.
* After chemotherapy, patients must be restaged prior to Step 1 registration using the same diagnostic work-up as required pre-chemotherapy. Repeat PET/CT or bone scan is not required. Patients must have:

* History/physical examination within 30 days of Step 1 registration;
* No CNS metastases (Repeat MRI required; see Section 3.2.3 for details) within 56 days prior to Step 1 registration;
* No progression in any site;
* Radiographic partial or complete response to chemotherapy in at least one disease site within 56 days prior to Step 1 registration.

1. If PET/CT was obtained prior to chemotherapy, either a repeat PET/CT or CT of the chest and abdomen with contrast can be obtained for response assessment.
2. Patients who underwent resection for limited-stage SCLC prior to chemotherapy and have no radiographically evident disease for response assessment remain eligible if post-chemotherapy imaging demonstrates no progression.
* Zubrod performance status 0-2
* Women of childbearing potential and male participants must practice adequate contraception
* Women of childbearing potential must have a negative qualitative serum pregnancy test =< 2 weeks prior to study entry
* Patients who are primary English or French speakers are eligible
* Patients must sign a study-specific informed consent prior to study entry
* PRIOR TO STEP 2 REGISTRATION
* The following baseline neurocognitive assessments must be completed and uploaded within 10 calendar days after or at the time of Step 1 registration: HVLT-R (recall, delayed recall, and recognition), TMT (Parts A and B), and COWA. The neurocognitive assessments will be uploaded into the NRG Oncology RAVE System for evaluation by Dr. Wefel. Once the upload is complete, within 3 business days, a notification email will be sent to the site to proceed to Step 2 registration. At minimum, the HVLT-R delayed recall must be able to be scored (i.e. completed without error) in order to be eligible.
* Patients must have a baseline raw score greater than 2 on the HVLT-R delayed recall

Exclusion Criteria:

* Prior radiotherapy to the head or neck (except for T1 glottic cancer), resulting in overlap of radiation fields
* Radiographic evidence of CNS metastases
* Radiographic evidence of hydrocephalus or other architectural distortion of the ventricular system, including placement of external ventricular drain or ventriculoperitoneal shunt
* Planned concurrent chemotherapy or anti-tumor agent during PCI

* Concurrent atezolizumab permitted
* Concomitant invasive malignancy or invasive malignancy within the past five years other than non-melanomatous skin cancer; history of in situ carcinoma (e.g. ductal carcinoma in situ of breast, in situ carcinoma of the cervix, vulva or larynx) is permitted
* Contraindication to MR imaging, such as implanted metal devices or foreign bodies or severe claustrophobia
* Severe, active comorbidity, defined as follows:

* Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months
* Transmural myocardial infarction within the last 6 months
* Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration
* Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects
* Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration
* Uncontrolled, clinically significant cardiac arrhythmias
* HIV positive with CD4 count < 200 cells/microliter;

1. Note: Patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count ≥ 200 cells/microliter within 30 days prior to Step 1 registration.
2. Note: HIV testing is not required for eligibility for this protocol.
* Pregnant or lactating women or women of childbearing potential and male participants who are sexually active and not willing/able to use medically acceptable forms of contraception