We investigated the effects of trial-to-trial, random variation in environmental forces on the motor adaptation of human subjects during reaching. Novel sequences of dynamic environments were applied to subjects' hands by a robot. Subjects reached first in a "mean field" having a constant gain relating force and velocity, then in a "noise field," having a gain that varied randomly between reaches according to a normal distribution with a mean identical to that of the mean field. The unpredictable nature of the noise field did not degrade adaptation as quantified by final kinematic error and rate of adaptation. To achieve this performance, the nervous system used a dual strategy. It increased the impedance of the arm as evidenced by a significant reduction in aftereffect size following removal of the noise field. Simultaneously, it formed an internal model of the mean of the random environment, as evidenced by a minimization of trajectory error on trials for which the noise field gain was close to the mean field gain. We conclude that the human motor system is capable of predicting and compensating for the dynamics of an environment that varies substantially and randomly from trial to trial, while simultaneously increasing the arm's impedance to minimize the consequence of errors in the prediction.