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.