Inclusion Criteria:

          1. Have histologically or cytologically confirmed stage IIIB (and not a candidate for
             definitive multimodality therapy) or stage four (IV) NSCLC.

          2. Must have documented ALK rearrangement.

          3. Have sufficient tumor tissue available for central analysis.

          4. Have at least 1 measurable (that is, target) lesion per RECIST v1.1.

          5. Recovered from toxicities related to prior anticancer therapy to National Cancer
             Institute (of the United States) (NCI) Common Terminology Criteria for Adverse Events
             (version 4.0) (CTCAE v 4.0) grade be less than or equal to (<=) 1.

          6. Are a male or female participants greater than or equal to (>=)18 years old.

          7. Have adequate organ function, as defined by the study protocol.

          8. Have Eastern Cooperative Oncology Group (ECOG) performance status <=2.

          9. Have normal QT interval on screening ECG evaluation, defined as QT interval corrected
             (Fridericia) (QTcF) of <= 450 millisecond (msec) in males or <=470 msec in females.

         10. For female participants of childbearing potential, have a negative pregnancy test
             documented prior to randomization.

         11. For female and male participants who are fertile, agree to use a highly effective form
             of contraception, as defined by the study protocol.

         12. Provide signed and dated informed consent indicating that the participants has been
             informed of all pertinent aspects of the study, including the potential risks, and is
             willingly participating.

         13. Have the willingness and ability to comply with scheduled visit and study procedures.

        Exclusion Criteria:

          1. Previously received an investigational antineoplastic agent for NSCLC.

          2. Previously received any prior tyrosine kinase inhibitor (TKI), including ALK-targeted
             TKIs.

          3. Previously received more than 1 regimen of systemic anticancer therapy for locally
             advanced or metastatic disease.

          4. Received chemotherapy or radiation within 14 days of first dose of study drug, except
             stereotactic radiosurgery (SRS) or stereotactic body radiation therapy (SBRT).

          5. Received anti-neoplastic monoclonal antibodies within 30 days of the first dose of
             study drug.

          6. Had major surgery within 30 days of the first dose of study drug, minor surgical
             procedures such as catheter placement or minimally invasive biopsies are allowed.

          7. Have been diagnosed with another primary malignancy other than NSCLC, except for
             adequately treated non-melanoma skin cancer or cervical cancer in situ; definitively
             treated non-metastatic prostate cancer; or participants with another primary
             malignancy who are definitively relapse-free with at least 3 years elapsed since the
             diagnosis of the other primary malignancy.

          8. Have symptomatic CNS metastases (parenchymal or leptomeningeal) at screening or
             asymptomatic disease requiring an increasing dose of corticosteroids to control
             symptoms within 7 days prior to randomization.

          9. Have current spinal cord compression (symptomatic or asymptomatic and detected by
             radiographic imaging). Participants with leptomeningeal disease and without cord
             compression are allowed.

         10. Be pregnant, planning a pregnancy, or breastfeeding.

         11. Have significant, uncontrolled, or active cardiovascular disease, as defined by the
             study protocol.

         12. Have uncontrolled hypertension.

         13. Have a history or the presence at baseline of pulmonary interstitial disease,
             drug-related pneumonitis, or radiation pneumonitis.

         14. Have an ongoing or active infection.

         15. Have a known history of human immunodeficiency virus (HIV) infection.

         16. Have a known or suspected hypersensitivity to brigatinib or its excipients and/or
             crizotinib or its excipients.

         17. Have malabsorption syndrome or other gastrointestinal (GI) illness or condition.

         18. Have any condition or illness that, in the opinion of the investigator, would
             compromise participant's safety or interfere with the evaluation of the study drug.