The purpose of this study is to evaluate the safety and efficacy of clobazam as adjunctive therapy in the treatment of seizures which lead to drop attacks (drop seizures) in subjects 2 to 30 years of age with Lennox-Gastaut Syndrome (LGS). Subjects will be enrolled at approximately 10 investigational sites in the U.S. for up to 15 weeks. Subjects will be randomly assigned to either a low dose or a high dose. The study will include a baseline period, a titration period and a maintenance period. After the maintenance period, subjects will either continue into an open-label extension study or enter the taper period with a final visit 1 week after the last dose.