This is a dose escalation study that will assess the safety of Vorinostat, a Histone Deacetylase (HDAC) inhibitor, in combination with palliative radiotherapy in patients with advanced or metastatic Non-Small Cell Lung Cancer (NSCLC). Vorinostat has been approved for use in patients with cutaneous T-cell lymphomas, but several pre-clinical studies suggest activity in lung cancer cell lines. Several HDAC inhibitors,including Vorinostat, may enhance the effect of radiotherapy, and this study will seek to confirm this.