We show that energy deposited into an expanding supernova remnant by a highly magnetic (B ~ 5 x 10^14 G) neutron star spinning at an initial period of P ~ 2-20 ms can substantially brighten the light curve. For magnetars with parameters in this range, the rotational energy is released on a timescale of days to weeks, which is comparable to the effective diffusion time through the supernova remnant. The late time energy injection can then be radiated without suffering overwhelming adiabatic expansion losses. The magnetar input also produces a central bubble which sweeps ejecta into an internal dense shell, resulting in a prolonged period of nearly constant photospheric velocity in the observed spectra. We derive analytic expressions for the light curve rise time and peak luminosity as a function of B, P and the properties of the supernova ejecta that allow for direct inferences about the underlying magnetar in bright supernovae. We perform numerical radiation hydrodynamical calculations of a few specific instances and compare the resulting light curves to observed events. Magnetar activity is likely to impact more than a few percent of all core collapse supernovae, and may naturally explain some of the brightest events ever seen (e.g., SN 2005ap and SN 2008es) at L > 10^44 ergs/s.
