Inclusion Criteria:

          -  Written informed consent on an Institutional Review Board (IRB)/Independent Ethics
             Committee (IEC)-approved ICF before any study-specific evaluation

          -  Histologically or cytologically confirmed metastatic or unresectable locally advanced
             NSCLC with EGFR activating mutation (excluding exon 20 insertion); measurable disease
             per RECIST 1.1

          -  Prior treatment with an EGFR TKI; in Phase 2, prior treatment with a T790M-directed
             EGFR TKI for patients in Group B. Previous chemotherapy is allowed; in Phase 2,
             immediate prior therapy must be EGFR TKI

          -  Patient willingness to undergo tumor biopsy at baseline and on treatment (optional for
             Phase 1; mandatory for Phase 2)

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0-1; life expectancy at
             least 3 months

          -  Adequate hematological and biological function; LVEF ≥50%

        Exclusion Criteria:

          -  Documented evidence in tumor of exon 20 insertion, small cell transformation, or MET
             amplification

          -  Leptomeningeal carcinomatosis or other untreated or symptomatic CNS metastases
             (asymptomatic CNS metastases allowed if clinically stable without requirement for
             steroids within 2 weeks)

          -  Known preexisting interstitial lung disease or pneumonitis

          -  Concurrent use of QT-prolonging medication

          -  Uncontrolled diabetes (HA1C > 10%) despite optional therapy

          -  Cardiac abnormalities:

               -  Clinically significant abnormal 12-lead ECG, QT interval corrected using
                  Fridericia's method (QTcF) >450 ms

               -  Inability to measure QT interval on ECG

               -  Personal or family history of long QT syndrome

               -  Implantable pacemaker or implantable cardioverter defibrillator

               -  Resting bradycardia < 55 beats/min

          -  Inability to swallow oral study treatment or any gastrointestinal disease or condition
             that would preclude adequate absorption of study treatment

          -  Presence of serious or unstable concomitant systemic disorder incompatible with the
             clinical study (eg, substance abuse; uncontrolled intercurrent illness including
             active infection; arterial thrombosis; unstable respiratory, hepatic, renal or cardiac
             disease; and other active malignancy)

          -  Pregnant or breastfeeding females and male or female patients who refuse to use
             adequate contraception during the study and for 16 weeks after the last dose of study
             treatment

          -  Any contraindication, allergy, or hypersensitivity to rociletinib, trametinib, or
             excipients