The trial consists of two 9-week studies—one study will enroll persons with hyperkalemic periodic paralysis and the other study will enroll persons with hypokalemic periodic paralysis. Participants will be randomly assigned to one of two treatment groups: dichlorphenamide or placebo (an inactive substance). During the studies, participants will be asked to keep a daily diary to record the time, length, and severity of each episode of weakness (attack). The study coordinator will contact participants weekly to review the diary information.