Safety and Efficacy of Belinostat When Used With Standard of Care Chemotherapy for Untreated Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically documented NSCLC confirmed. * Has advanced NSCLC (Stage IV), not previously treated with any chemotherapy regiment (prior adjuvant chemotherapy and/or chemotherapy/radiation for Stage III allowed). * Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>20 mm with conventional techniques or as \>10 mm with spiral CT scan. * Life expectancy of \> 3 months * Must have returned to baseline or grade 1 adverse event from any acute toxicity related to prior therapy * Adequate immune and multisystem organ function (as evidenced by urine and blood values within specified parameters). Exclusion Criteria: * Brain or meningeal metastases. Note, patients with adequately treated brain metastases, e.g. surgically resected, or adequately controlled by radiotherapy, with no residual neurological symptoms due to metastases and no steroid treatment required, can be enrolled. If clinical suspicion, adequate investigations should be performed to rule out brain metastases or meningeal involvement. * History of a previous malignancy within 5 years with the exception of non-metastatic non-melanoma skin cancer or cervical carcinoma in situ. Prior systemic therapy for other malignancy must be completed at least 5 years before treatment is allowed. * Lung carcinoma of squamous cell histology (mixed tumors will be categorized by the predominant cell type unless small cell elements are present, in which case the patient is ineligible; sputum cytology alone is not acceptable). * History of hemoptysis within 3 months prior to enrollment * Current or recent (within 10 days of enrollment) use of aspirin (\>325 mg/day) or chronic use of other non-steroidal anti-inflammatory medications. * Prior systemic anti-tumor therapy for Stage IV lung cancer. Note, prior radiotherapy is allowed provided treatment was completed at least 2 weeks before enrollment. Prior surgery is allowed if completed at least 4 weeks before enrollment. * Treatment with investigational agents within the 2 weeks prior to enrollment. * Significant vascular disease (e.g., aortic aneurysm, history of aortic dissection) or clinically significant peripheral vascular disease. * Hypertension not controlled by medical therapy. * Significant cardiovascular disease, myocardial infarction within the past 6 months, unstable angina, unstable arrhythmia or a need for anti-arrhythmic therapy (use of medication to control heart rate in patients with atrial fibrillation is allowed, if stable medication for at least last month prior to enrollment, or evidence of acute ischemia on electrocardiogram). * Marked baseline prolongation of QT/QTc interval that required use of concomitant medication that may cause Torsade de Pointes * Significant, non-healing wounds, acute or non-healing ulcers, or bone fractures within 3 months of fracture. * Undergone major surgery within 4 weeks of planned initiation of cycle 1. * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of enrollment. * History of any gastrointestinal bleeding within the 3 months prior to enrollment. * Known hypersensitivity to either platinum compounds or paclitaxel, or any components of the study medications, and inability for desensitization. * Peripheral neuropathy NCI ≥ Grade 2. * Co-existing active severe infection or any co-existing medical condition likely to interfere with trial procedures. * Known infection with HIV, or known active Hepatitis B or C infection. * Pregnant or lactating. * not willing to use effective contraception during the study and until 6 months post-completion of last cycle administered