• Histologically or cytologically-confirmed diagnosis of advanced or recurrent (Stage IIIB/C not amenable for radical treatment) or metastatic (Stage IV) NSCLC that harbors a documented ROS1 gene rearrangement.

• No prior treatment with a ROS1 tyrosine kinase inhibitor, chemotherapy or other systemic therapy for advanced or recurrent (Stage IIIB/C not amenable for radical treatment) or metastatic (Stage IV) NSCLC

• Prior radiotherapy is allowed if more than 14 days have elapsed between the end of treatment and randomization

• Measurable systemic disease according to RECIST v1.1

• Participants with measurable and non-measurable CNS lesions per RECIST v1.1, including leptomeningeal carcinomatosis

• Life expectancy of at least 12 weeks

• Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2

• Adequate hematologic, renal, liver functions

• Participants must have recovered from effects of any major surgery or significant traumatic injury at least 28 days before the first dose of study treatment

• Ability to swallow entrectinib and crizotinib intact without chewing, crushing, or opening the capsules

• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \<1% per year during the treatment period and for up to 5 weeks after the last dose of entrectinib or for at least 90 days after the last dose of crizotinib

• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm.