Dabrafenib is a potent and selective inhibitor of BRAF kinase activity. This is a Phase II, non-randomized, open-label study to assess the efficacy, safety, and tolerability of dabrafenib administered as a single agent and in combination with trametinib in stage IV disease to subjects with BRAF mutant advanced non-small cell lung cancer. Subjects will receive dabrafenib 150 mg twice daily (BID) in monotherapy treatment and dabrafenib 150 mg bid and trametinib 2 mg once daily in combination therapy and continue on treatment until disease progression, death, or unacceptable adverse event.