The goal of this clinical research study is to find out how well the drug Zolinza (vorinostat) works in combination with the drug combination called CHOP (cyclophosphamide, doxorubicin, vincristine, and prednisone) to treat patients with untreated T-cell Non-Hodgkin's Lymphoma (NHL). The safety of these drugs in combination and the best dose of vorinostat when given in combination with CHOP will also be studied.

The Study Drugs:

Vorinostat is designed to cause chemical changes in different groups of proteins that are attached to DNA (the genetic material of cells), which may slow the growth of cancer cells or cause the cancer cells to die.

Cyclophosphamide is designed to interfere with the multiplication of cancer cells, which may slow or stop their growth. This may cause the cancer cells to die.

Doxorubicin is designed to stop the growth of cancer cells, which may cause the cells to die.

Vincristine is designed to interfere with the multiplication of cancer cells, which may slow or stop their growth. This may cause the cancer cells to die.

Prednisone is designed to decrease inflammation by preventing white blood cells from completing an inflammatory reaction. This drug can cause lymphocytes, a type of white blood cell, to break apart and die.

Study Drug Administration:

If you are found to be eligible to take part in this study, you will begin to take vorinostat on the first day of treatment which is Day -1. Vorinostat capsules are taken by mouth, either 3 times a day or 2 times a day, depending on what the study doctor thinks is in your best interest. If you are taking vorinostat 3 times a day, it should be taken in the morning, afternoon and evening. If you are taking vorinostat 2 times a day, you will take the capsules in the morning and evening. The capsules must be taken with food (within 30 minutes after a meal). You will receive the vorinostat capsules on the first day of each cycle. You will also receive instructions on how to take the drug. You should return any unused vorinostat capsules back to study staff at the end of each cycle. You will take vorinostat for 5 days (Days -1 through 3) of each cycle and then beginning on Day 1, cyclophosphamide, vincristine, and doxorubicin will be given though a needle in your vein. This will happen for each 21-day study cycle. Cyclophosphamide is given over 1 hour. Vincristine is given over 15 minutes. Doxorubicin is also given over 15 minutes.

The starting dose of vorinostat may change On Days 1-5 of each cycle, you will take prednisone tablets by mouth.

If you begin to experience severe or intolerable side effects, the study drug schedule may be stopped for up to 3 weeks. If the side effects improve, you may be able to receive the study drugs again, with either a lower dose of vorinostat or if you are taking vorinostat three times daily, you may take it twice a day instead. The chemotherapy drugs (cyclophosphamide, doxorubicin, vincristine, and prednisone) may also be lowered depending on what side effects are being experienced. If you continue to have severe or intolerable side effects with the lower dose of vorinostat and chemotherapy, you will taken off study.

Study Visits:

On Day 1 of all cycles, the following tests and procedures will be performed:

• Your medical history will be recorded, including any drugs that you are taking.
• You will be asked about any side effects you may have experienced.
• You will have a physical exam, including measurement of your vital signs and weight.
• Blood (about 5 teaspoons) will be drawn for routine tests.
• Your performance status will be recorded.

On Day 1 of Cycle 2 you will have an ECG.

On or before Day 1 of Cycle 3 the following tests and procedures will be performed if your doctor thinks necessary:

• You will have CT and/or PET scans to check the status of the disease.
• You may have a bone marrow aspirate and/or biopsy to check the status of the disease.

Length of Study:

You will receive the study drugs for up to 6 cycles. You may be taken off study early if the disease gets worse or if severe or intolerable side effects occur.

End-of-Study Visit:

If you go off study treatment for any reason, you will have an end-of-study visit within 4 weeks after your last dose of study drugs or before starting a new treatment. At this visit, the following tests and procedures will be performed:

• You will have a physical exam, including measurement of your vital signs.
• Your performance status will be recorded.
• You will be asked about any side effects you may have experienced.
• Blood (about 5 teaspoons) will be drawn for routine tests.
• You will have CT scans and PET scans to check the status of the disease.
• If you had skin lesions when you began the study, the skin lesions will be photographed.
• If the doctor thinks it is needed, you will have bone marrow biopsy and/or aspirate.

Follow-up Visits:

After you are off study treatment, you will have follow-up visits. You will go to these visits every 3 months for the1st year, every 4 months for the 2nd and 3rd years, and every 6 months for the 4th and 5th years. After this, you will return 1 time each year unless the lymphoma returns. The following tests and procedures will be performed:

• You will have a physical exam, including measurement of your vital signs.
• Your performance status will be recorded
• You will be asked about any side effects you may have experienced.
• Blood (about 5 teaspoons) will be drawn for routine tests.
• You will have CT scans and PET scans to check the status of the disease.
• If you had skin lesions when you began the study, the skin lesions will be photographed.
• If the doctor thinks it is needed, you will have bone marrow biopsy and/or aspirate.

This is an investigational study. Vorinostat is FDA approved and commercially available for the treatment of cutaneous T-cell lymphoma that has not come back or not responded to prior therapy. CHOP is currently FDA approved for treatment of patients with NHL. The use of vorinostat in combination with CHOP in patients with T-cell NHL is investigational.

Up to 52 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients must have a new diagnosis of T-cell NHL eligible histologies include:Peripheral T-cell lymphoma (unspecified), CD 30 + anaplastic large cell lymphoma (ALK) (ALK-1 positive and ALK-1 negative), angioimmunoblastic T-cell lymphoma, intestinal T-cell lymphoma, subcutaneous panniculitic T-cell lymphoma.
2. Patients who are eligible for blood and marrow transplant can receive this treatment to maximal reduction of tumor bulk. A minimum of four cycles of therapy will be given before evaluation for to hematopoetic stem cell transplant.
3. Patients must have biopsy proven disease which can include bone marrow and/or lymph node (cutaneous only disease is excluded)
4. Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
5. Patients must be age 18 years old and above.There is no dosing or adverse event data are currently available on the use of vorinostat in patients <18 years of age, children are excluded from this study but may be eligible for future pediatric phase 2 combination trials.
6. There is Patients are required to have adequate bone marrow reserve as indicated: Absolute neutrophil count (ANC) >/= 1000/mm^3, Platelets >/= 50,000/mm3, Hemoglobin >/= 8g/dL. If there is bone marrow involvement by lymphoma then there is no minimum level of counts required.
7. Patients must have adequate liver function as indicated by: Bilirubin </= 1.5 times the upper limit of normal (ULN), Alanine transaminase (ALT) </=2 times the (ULN) or aspartate transaminase (AST) </= 2 times the ULN. These values must be obtained within two weeks before protocol entry.
8. Patients are required to have adequate renal function as indicated by a serum creatinine </= 2.5 mg/dL. This value must be obtained within two weeks before protocol entry.
9. Left ventricular ejection fraction must be evaluated by nuclear medicine scan or echocardiography and measure >/= 50%.
10. Concomitant steroids may continue provided they are being used for symptom management and not for treatment of lymphoma.
11. Male patients must agree to use a barrier method of contraception or agree to abstain from heterosexual activity for the duration of the study
12. Female patients must be willing to use two adequate barrier methods of contraception to prevent pregnancy or agree to abstain from heterosexual activity throughout the study or be post menopausal (free from menses > two years or surgically sterilized).
13. Female patients of childbearing potential must have a negative serum pregnancy test (Beta human chorionic gonadotropin (hCG)) within 72 hours of receiving the first dose of vorinostat.
14. Patients must have the ability able to give informed consent.

Exclusion Criteria:

1. 1. Patients with a) T-cell lymphoma with skin involvement only are excluded if they have no evidence of systemic disease b)T-cell prolymphocytic leukemia (T-PLL) c) T-cell large granular lymphocytic leukemia d) Primary cutaneous CD30+ disorders: anaplastic large cell lymphoma and lymphomatoid papulosis e) Angiocentric/nasal type T/Natural Killer (NK)-cell lymphoma f) Hepatosplenic gamma-delta T-cell lymphoma
2. Patients with active Hepatitis B and/or Hepatitis C infection.
3. Patients with known HIV infection are excluded. a) These patients are excluded secondary to potential to target activated T-cells, in a population of patients already at risk for T-cell depletion, would be a contraindication to therapy.
4. Patients with active infections requiring specific anti-infective therapy are not eligible until all signs of infections are resolved.
5. Patients with pre-existing cardiovascular disease requiring ongoing treatment. This includes:a) Congestive heart failure, b) Severe CAD, c) Cardiomyopathy, d) Uncontrolled cardiac arrhythmia, e) Unstable angina pectoris, f) Recent MI (within 6 months).
6. Patients with prior exposure to either vorinostat (including other histone deacetylase (HDAC) inhibitors except valproic acid) or anthracyclines: a) Patients who have received valproic acid (VPA) for the treatment of seizures may be enrolled on this study, but must not have received VPA within 30 days of study enrollment.
7. Patients who are pregnant or breast-feeding. a)Effects of this treatment on the fetus and young children are unknown at this time.
8. Patients who have had an invasive solid tumor malignancy in the past five years except non-melanoma skin cancers or cervical carcinoma in situ or ductal/lobular carcinoma in situ of the breast who is currently without evidence of disease.
9. Patients undergoing anti-neoplastic chemotherapy, radiation, hormonal (excluding contraceptives) or immunotherapy, or investigational medications within the past four weeks.
10. Patients with deep vein thrombosis within three months.
11. Patient with concurrent use of complementary or alternative medicines.
12. Patients with psychiatric illness and/or social situations that would limit compliance with the study medication and requirements.
13. Patients with grade 2 or more neuropathy.
14. Patients with known central nervous system (CNS) lymphoma.

Adverse event reporting period begins once study drug treatment is initiated through 30 days after the last study treatment (21 day cycle). Overall study participation July 2009 to August 2012 for Phase I (Schedule A) and Phase II (Schedule B).