Inclusion Criteria:

- Histologically or cytologically proven diagnosis of NSCLC

- Inoperable Stage IIIA or IIIB (excluding malignant pleural effusion) disease
according to the American Joint Committee on Cancer (AJCC) Cancer Staging Manual,
Sixth edition (2002)

- At least one site of measurable disease, as defined by the modified Response
Evaluation Criteria In Solid Tumors (RECIST) criteria

- Eastern Cooperative Oncology Group (ECOG) performance status 0-2

- Inability to tolerate full dose cisplatin as defined by:

- Creatinine clearance less than 50ml/min

- Greater than grade 2 sensory hearing loss (as defined by National Cancer Institute
[NCI] Common Terminology Criteria for Adverse Events [CTCAE] criteria v3.0 adverse
event term "Hearing: Patients without baseline audiogram and not enrolled in a
monitoring program")

- Performance status >= 2

- Age >= 75 years

- Cardiac history, such as myocardial infarction within 6 months, angina, or heart
disease as defined by the New York Heart Association (NYHA) Class III or IV

- Any other comorbid disease or condition that would increase the risk of toxicity of
cisplatin therapy

- Female patient is either post menopausal, free from menses for >= 2 years, surgically
sterilized or willing to use 2 adequate barrier methods of contraception to prevent
pregnancy or agrees to abstain from heterosexual activity throughout the study

- Female patient of childbearing potential has a negative serum pregnancy test
beta-human chorionic gonadotropin (hCG) within 7 days prior to receiving the first
dose of vorinostat

- Male patient agrees to use an adequate method of contraception for the duration of
the study

- Absolute neutrophil count (ANC) >= 1,500/mcL

- Platelets >= 100,000/mcL

- Hemoglobin >= 9 g/dL

- Prothrombin Time or International Normalized Ratio (INR) =< 1.5x upper limit of
normal (ULN) unless receiving therapeutic anticoagulation

- Partial thromboplastin time (PTT) =< 1.2 times the ULN unless the patient is
receiving therapeutic anticoagulation

- Potassium levels: Normal limits

- Magnesium levels: Normal limits

- Calculated creatinine clearance >= 20 mL/min

- Serum total bilirubin =< 1.5 X ULN

- Aspartate aminotransferase (AST) (serum glutamate oxaloacetic transaminase [SGOT])
and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =<
2.5 X ULN

- Alkaline Phosphatase =< 2.5 X ULN

- Patient, or the patient's legal representative, has voluntarily agreed to participate
by giving written informed consent

- Patient has a life expectancy of at least 12 weeks

- Patient is available for periodic blood sampling, study related assessments, and
management at the treating institution for the duration of the study

Exclusion Criteria:

- Patient who has had chemotherapy, radiotherapy, or biological therapy for NSCLC
within 5 years prior to initial dosing with study drug(s)

- Symptomatic neuropathy (>= grade 2)

- Patient is currently participating or has participated in a study with an
investigational compound or device within 30 days of initial dosing with study
drug(s)

- Patient had prior treatment with an histone deacetylases (HDAC) inhibitor (e.g.,
romidespsin [Depsipeptide, NSC-630176], entinostat [MS 275], dacinostat [LAQ-824],
belinostat [(PXD-101]), panobinostat [LBH589], mocetinostat [MGCD0103], CRA024781,
etc); patients who have received compounds with HDAC inhibitor-like activity, such as
valproic acid, as anti-tumor therapy should not enroll in this study; patients who
have received such compounds for other indications, e.g., valproic acid for epilepsy,
may enroll after a 30-day washout period

- Patient has known hypersensitivity to the components of study drug or its analogs or
paclitaxel

- NYHA Class III or IV congestive heart failure, myocardial infarction within the
previous 6 months, QTc > 0.47 seconds, or uncontrolled arrhythmia

- Patient is pregnant or breast feeding, or expecting to conceive or father children
within the projected duration of the study

- Patient with a "currently active" second malignancy, other than non-melanoma skin
cancer and carcinoma in situ of the cervix, should not be enrolled; patients are not
considered to have a "currently active" malignancy if they have completed therapy for
a prior malignancy, are disease free from prior malignancies for > 5 years or are
considered by their physician to be at less than 30% risk of relapse

- Patient has a history or current evidence of any condition, therapy, or lab
abnormality that might confound the results of the study, interfere with the
patient's participation for the full duration of the study or is not in the best
interest of the patient to participate