The smart grid introduces concerns for the loss of consumer privacy; recently deployed smart meters retain and distribute highly accurate profiles of home energy use. These profiles can be mined by Non Intrusive Load Monitors (NILMs) to expose much of the human activity within the served site. This paper introduces a new class of algorithms and systems, called Non-Intrusive Load Leveling (NILL) to combat potential invasions of privacy. NILL uses an in-residence battery to mask variance in load on the grid, thus eliminating exposure of the appliance-driven information used to compromise consumer privacy. We use real residential energy use profiles to drive four simulated deployments of NILL. The simulations show that NILL exposes only 1.1 to 5.9 useful energy events per day hidden amongst hundreds or thousands of similar battery-suppressed events. Thus, the energy profiles exhibited by NILL are largely useless for current NILM algorithms. Surprisingly, such privacy gains can be achieved using battery systems whose storage capacity is far lower than the residence's aggregate load average. We conclude by discussing how the costs of NILL can be offset by energy savings under tiered energy schedules.