A smart meter (SM) periodically measures end-user electricity consumption and reports it to a utility provider (UP). Despite the advantages of SMs, their use leads to serious concerns about consumer privacy. In this paper, SM privacy is studied by considering the presence of an energy harvesting device (EHD) as a means of masking the user's input load. The user can satisfy part or all of his/her energy needs from the EHD, and hence, less information can be leaked to the UP via the SM. The EHD is typically equipped with a rechargeable energy storage device, i.e., a battery, whose instantaneous energy content limits the user's capability in covering his/her energy usage. Privacy is measured by the information leaked about the user's real energy consumption when the UP observes the energy requested from the grid, which the SM reads and reports to the UP. The minimum information leakage rate is characterized as a computable information theoretic single-letter expression when the EHD battery capacity is either infinite or zero. Numerical results are presented for a discrete binary input load to illustrate the potential privacy gains from the existence of a storage device.