We report the results of Keck L-band non-redundant aperture masking of HR 8799, a system with four confirmed planetary mass companions at projected orbital separations of 14 to 68 AU. We use these observations to place constraints on the presence of planets and brown dwarfs at projected orbital separations inside of 10 AU---separations out of reach to more conventional direct imaging methods. No companions were detected at better than 99% confidence between orbital separations of 0.8 to 10 AU. Assuming an age of 30 Myr and adopting the Baraffe models, we place upper limits to planetary mass companions of 80, 60, and 11 Jupiter Masses at projected orbital separations of 0.8, 1, and 3-10 AU respectively. Our constraints on massive companions to HR 8799 will help clarify ongoing studies of the orbital stability of this multi-planet system, and may illuminate future work dedicated to understanding the dust-free hole interior to ~6 AU.