We report the discovery of two extremely low luminosity globular clusters in the Milky Way halo. These objects were detected in the Sloan Digital Sky Survey Data Release 5 and confirmed with deeper imaging at the Calar Alto Observatory. The clusters, Koposov 1 and Koposov 2, are located at ~40-50 kpc and appear to have old stellar populations and luminosities of only M_V ~ -1 mag. Their observed sizes of ~3 pc are well within the expected tidal limit of ~10 pc at that distance. Together with Palomar 1, AM 4, and Whiting 1, these new clusters are the lowest luminosity globular clusters orbiting the Milky Way, with Koposov 2 the most extreme. Koposov 1 appears to lie close to distant branch of the Sagittarius stream. The half-mass relaxation times of Koposov 1 and 2 are only ~70 and ~55 Myr respectively (2 orders of magnitude shorter than the age of the stellar populations), so it would seem that they have undergone drastic mass segregation. Since they do not appear to be very concentrated, their evaporation timescales may be as low as ~0.1t_Hubble. These discoveries show that the structural parameter space of globular clusters in the Milky Way halo is not yet fully explored. They also add, through their short remaining survival times, significant direct evidence for a once much larger population of globular clusters.