We present a new, magnetohydrodynamic mechanism for inflation of close-in giant extrasolar planets. The idea behind the mechanism is that current, which is induced through interaction of atmospheric winds and the planetary magnetic field, results in significant Ohmic dissipation of energy in the interior. We develop an analytical model for computation of interior Ohmic dissipation, with a simplified treatment of the atmosphere. We apply our model to HD209458b, Tres-4b, and HD189733b. With conservative assumptions for wind speed and field strength, our model predicts a generated power that appears to be large enough to maintain the transit radii, opening an unexplored avenue toward solving a decade-old puzzle of extrasolar gas giant radius anomalies.