The purpose of this study is to determine whether a painless and noninvasive procedure called transcranial direct current stimulation (tDCS) combined with a method of physical therapy called constraint-induced movement therapy improves motor function in patients with chronic stroke. Research in healthy subjects has shown that when tDCS is combined with motor learning tasks, there is an increase in learning as compared to motor learning tasks only. The tDCS procedure sessions will be compared to sham (fake) procedure sessions, which is also called placebo stimulation. This study is double blind, which means neither the subjects nor researchers analyzing motor function will know if participants are receiving real tDCS stimulation or placebo. Only the person performing the procedure will know which one participants are receiving. Only by comparing the tDCS procedure to a sham (placebo) procedure can we understand if the tDCS actually improves motor function.