This will be a single center phase I dose escalation trial. LBH589 will be administered orally twice weekly. Gemcitabine will be administered intravenously over 30 minutes on days 1, 8, and 15 every 28 days. Dose escalation will begin at Dose Level 1. Three patients will be enrolled at each dose level. If 1/3 patients experiences dose-limiting toxicity, the dose level will be expanded to 6 patients. If 2/6 patients experience dose-limiting toxicity at a specific dose level, then the previous dose level will be considered the recommended phase II dose. Dose escalation will continue until the maximum tolerated dose is determined or until all dose levels outlined in the protocol have been completed. A total of 10 patients will be treated at the dose that is recommended for further phase II evaluation to further assess the safety of the combination regimen. Toxicity assessments will be ongoing and disease assessments will be repeated every 2 treatment cycles. Patients will be allowed to continue on study until disease progression unless toxicity warrants drug discontinuation.