A Study of Nivolumab +/- Nab-paclitaxel in Non-small Cell Lung Cancer

Inclusion Criteria: 1. Histologically or cytologically confirmed, Stage IV non-small cell lung cancer (per the Union Internationale contre le Cancer/American Join Committee on Cancer staging system, 7th edition) or recurrent incurable non-small cell lung cancer that has progressed after first-line chemotherapy. 2. Prior Therapy: Platinum doublet chemotherapy for current diagnosis of advanced lung cancer. Only one prior line of chemotherapy for advanced lung cancer allowed. Adjuvant chemotherapy, neoadjuvant chemotherapy, or chemoradiotherapy given for early stage lung cancer at least 6 months prior to diagnosis of recurrent/metastatic disease is not counted as a line of therapy for advanced lung cancer. Patients who received platinum doublet therapy with or without radiotherapy as part of treatment for early stage non-small cell lung cancer less than 6 months after developing stage 4 or recurrent incurable disease will be considered study eligible by the criterion of having received one line of chemotherapy for non-small cell lung cancer. 3. EGFR, ALK and ROS biomarker positive tumors are eligible as long as the patient has received at least one standard oral, molecular inhibitor therapy in addition to standard platinum doublet chemotherapy. More than one molecular inhibitor is allowed such as a first generation EGFR inhibitor followed by a next generation EGFR inhibitor when T790 mutation develops. Prior molecular therapy for biomarker positive tumors such as (but not limited to) MET, RET and BRAF allowed but not required. 4. Prior chemotherapy must have been completed 21 days prior to initiation of protocol therapy and all toxicities must \< grade 2. 5. Patients must have \< Grade 2 or pre-existing neuropathy (per CTCAE). 6. Palliative radiation must have been completed 2 weeks prior to the initiation of study therapy. 7. All patients must have measurable disease. Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20mm with conventional techniques or as ≥10mm with spiral CT scan. 8. ECOG Performance Status: 0-1 9. Second malignancy: No "currently active" second malignancy other than non-melanoma skin cancers. 10. Brain metastases: brain metastases must have been treated at least 2 weeks prior to enrollment, be asymptomatic from brain metastases, stable on brain imaging, and not be receiving a supra-physiologic dose of steroids (\> 10 mg prednisone daily or equivalent). 11. Non-pregnant and non-nursing. The effect of nab-paclitaxel and nivolumab on the fetus is unknown. 12. Women of childbearing potential (WOCBP) must be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 6 months after the last dose of study medication. Patients of childbearing potential are those who have not been surgically sterilized or have not been free of menses \> 1 year. 13. Male patients must agree to use an adequate method of contraception starting with the first dose of study therapy through 7 months after the last dose of study therapy. 14. Age ≥18 years. 15. Required Initial Laboratory Values: Leukocytes ≥2000/ µl Hemoglobin \>9.0 g/dL Platelets ≥100,000/ µl ANC ≥1,500/mcL Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 40 mL/min (if using the Cockcroft-Gault formula below): Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL Male CrCl = (140 - age in years) x weight in kg x 1.00 Total Bilirubin \<1.5 mg/dl (except for subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dl) SGOT (AST) \<2.5 x ULN ALP \<2.5 x ULN in absence of liver metastases (\<5 x ULN if liver metastases present PTT \<1.5 x ULN 16. An archival tumor sample from either a prior core needle biopsy or surgical specimen must be available to be submitted for correlative studies as an eligibility requirement prior to registration. The sample must be shipped within 6 weeks of enrollment. Participants without an available archival tumor sample are considered ineligible. Exclusion Criteria: 1. Prior nab-paclitaxel chemotherapy excluded. 2. Prior immune therapy for NSCLC excluded. Patients should be excluded if they have had prior treatment with an anti-PD-1, anti-PD-L1, anti PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways. 3. Patients will be excluded if they have an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. 4. Patients will be excluded if they have a condition requiring systemic treatment with either corticosteroids (\>10mg/day prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \>10 mg daily prednisone equivalents are permitted in the absence or active autoimmune disease. 5. Patients should be excluded if they test positive for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. 6. Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). 7. Allergies and Adverse Drug Reaction: History of allergy to study drug components