We report the discovery of OH masers and positionally resolved H_2_O maser emission in the nucleus of NGC 1068. The brightest H_2_O masers are associated with the radio continuum component that is probably the location of the central engine (Gallimore, Muxlow, and coworkers). These masers trace a ~50 mas (~5 pc) roughly linear velocity gradient along P.A 94^deg^ +/- 4^deg^, which is almost at right angles to the local radio jet axis. The kinematics of the masers are well described as an edge-on Keplerian disk surrounding a large central mass concentration (black hole?). The inner radius of the maser disk is ~> 1.3 pc, and the outer radius is ~2.5 pc, assuming a distance of 22 Mpc. The mass within the inner radius, normalized to the best-fit disk parameters, is 4.4 x 10^7^ M_sun_ x (r_in_/1.3 pc) (ν_max_/378 km s^-1^)^2^. These masers might occur in the parsec-scale torus thought to obscure the central engine. Radio continuum emission fills the region interior to the H_2_O masers, in agreement with the prediction that the continuum emission is thermal free-free radiation from the inner face of the molecular torus (Gallimore and coworkers). The location of-the OH masers and nuclear H I absorption (Gallimore and coworkers), measured with ~1" angular resolution, is consistent with the location of the H_2_O masers associated with the central engine. The H I absorption profile is also consistent with the Keplerian model for the H_2_O maser disk kinematics, and the velocity range of the OH masers is similar to that spanned by both the H I and H_2_O spectral features. It therefore seems likely that the OH masers and H I absorption also originate in the obscuring material surrounding the central engine. The OH masers indicate the presence of a more tenuous molecular medium in the torus, in addition to the denser material traced by the H_2_O maser emission. We have also discovered fainter H_2_O masers located 0.3" (~30 pc) downstream along the radio jet. These masers are too distant from the central engine to arise in a parsec-scale torus. They may instead occur at the shock interface between the radio jet and an intervening molecular cloud. The implication is that H_2_O magamaser emission may probe both circumnuclear disks and shock fronts in other active galactic nuclei.