Inclusion Criteria:  Subjects must have signed and dated an IRB/IEC approved written informed consent form in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol related procedures that are not part of normal subject care. Subjects must be willing and able to comply with scheduled visits, treatment schedule, and laboratory testing. Patients diagnosed with histologically or cytologically confirmed locally advanced not eligible to a local treatment or metastatic NSCLC (Stage IIIB, IIIC or IV accordingly to 8th classification TNM, UICC 2015). Patients are eligible for trial entry on the basis of locally determined ALK testing. ALK Immunohistochemistry (IHC) assay (3+ only), DNA-based or RNA-based next generation sequencing (NGS) assay or nCounter Nanostring assay performed locally are accepted ALK testing assays after review by the promotor. If ALK rearrangement diagnostic is performed using IHC and the result is + or 2+, a confirmation with a second method performed locally (DNA-based or RNA-based next generation sequencing (NGS) assay, nCounter Nanostring assay or ALK FISH performed) is required. All Patients must have at least one measurable target lesion according to RECIST v1.1 per investigator assessment. The radiological assessment has to be done within the timelines indicated. Patients with asymptomatic and neurologically stable CNS metastases (including patients controlled with less than 10mg/day of methylprednisolone within the last week prior to study entry) will be eligible. Tumor Sample Requirement: sufficient tumor tissue for central analysis should be available (tumor block or a minimum of 10 unstained slides of 4 µm of analyzable tissue). Age ≥18 years. Life expectancy of at least 12 weeks, in the opinion of the Investigator. Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1. Adequate Bone Marrow Function, including: Absolute Neutrophil Count (ANC) ≥1.5 x 109/L; Platelets ≥100 x 109/L; Hemoglobin ≥9 g/dL. Adequate Pancreatic Function, including: Serum lipase ≤1.5 ULN. Adequate Renal Function, including: Estimated creatinine clearance ≥45 mL/min as calculated using the standard method of the institution. Adequate Liver Function, including: Total serum bilirubin ≤1.5 x ULN (<3.0 × ULN for patients with Gilbert syndrome); Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) ≤2.5 x ULN; ≤5.0 x ULN if there is liver metastases involvement. Participants must have recovered from toxicities related to prior anticancer therapy to CTCAE Grade ≤ 1. Participants must have recovered from effects of any major surgery, or significant traumatic injury, at least 35 days before the first dose of treatment. Have normal QT interval on screening ECG evaluation, defined as QT interval corrected (Fridericia) (QTcF) of ≤450 milliseconds (msec) in males or ≤470 msec in females. Female patients who: are postmenopausal for at least 1 year before the screening visit, OR are surgically sterile, OR if they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, one of them being nonhormonal, from the time of signing the informed consent through 6 months after the last dose of study drug, or agree to completely abstain from heterosexual intercourse. Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: agree to practice effective barrier contraception during the entire study treatment period and through 6 months after the last dose of study drug, or agree to completely abstain from heterosexual intercourse. Willingness and ability to comply with the study scheduled visits, treatment plans, laboratory tests and other procedure. Participant has national health insurance coverage.  Exclusion Criteria:  Previously received an investigational antineoplastic agent for NSCLC. Previously received any prior TKI, including ALK-targeted TKIs. Known molecular co-alteration i.e. activating EGFR/BRAF/KRAS/MET mutation and ROS1/RET/NTRK fusion. Previously received neo-adjuvant or adjuvant systemic chemotherapy or consolidation immunotherapy if completion of (neo) adjuvant/consolidation therapy occurred <12 months prior to randomization. Patients who have leptomeningeal disease (LM) or carcinomatous meningitis (CM) according to MRI data and/or in case of documented cerebral spinal fluid (CSF) positive cytology. Spinal cord compression. Patients with symptomatic or neurologically instable CNS metastases. Major surgery within 30 days of study entry. Minor surgical procedures (e.g., port insertion, mediastinoscopy, surgical procedure for re-sampling) are not excluded, but sufficient time at investigator discretion should have passed for wound healing. Radiation therapy within 2 weeks of study entry. Stereotactic or small field brain irradiation must have completed at least 2 weeks prior to study entry. Whole brain radiation must have completed at least 4 weeks prior to study entry. Active and clinically significant bacterial, fungal, or viral infection including hepatitis B (HBV), hepatitis C (HCV), known human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS)-related illness. Have significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to: a) myocardial infarction within 6 months prior to the first dose of study drug; b) unstable angina within 6 months prior to the first dose of study drug; c) congestive heart failure within 6 months prior to the first dose of study drug; d) any history of ventricular arrhythmia; e) history of clinically significant atrial arrhythmia or clinically significant bradyarrhythmia as determined by the treating physician; f) cerebrovascular accident or transient ischemic attack within 6 months prior to the first dose of study drug. Have uncontrolled hypertension. Patients with hypertension should be under treatment on study entry to control blood pressure. History of grade 3 or 4 of interstitial fibrosis or interstitial lung disease including a history of pneumonitis, hypersensitivity pneumonitis, interstitial pneumonia, interstitial lung disease, obliterative bronchiolitis, pulmonary fibrosis and radiation pneumonitis. Presence of interstitial fibrosis of any grade at baseline. Other severe acute or chronic medical or psychiatric condition, including recent (within the past year) or active suicidal ideation or behavior, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. Evidence of active malignancy (other than current NSCLC, non-melanoma skin cancer, in situ cervical cancer, papillary thyroid cancer, DCIS of the breast or localized and presumed cured prostate cancer) within the last 3 years. Active inflammatory gastrointestinal disease, malabsorption syndrome, chronic diarrhea, symptomatic diverticular disease or previous gastric resection or lap band. Current use or anticipated need for food or drugs prohibited. Patients presenting with abnormal Left Ventricular Ejection Fraction (LVEF) by echocardiogram or Multi-Gated Acquisition Scan (MUGA) according to institutional lower limits. Have a known or suspected hypersensitivity to brigatinib, carboplatin or pemetrexed or their excipients. Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug. Received systemic treatment with strong cytochrome p-450 (cyp)3a inhibitors, strong cyp3a inducers, or moderate cyp3a inducers within 14 days before enrolment.