  In this article we construct the chirality and Dirac operators on
noncommutative AdS_2. We also derive the discrete spectrum of the Dirac
operator which is important in the study of the spectral triple associated with
AdS_2. It is shown that the degeneracy of the spectrum present in the
commutative AdS_2 is lifted in the noncommutative case. The way we construct
the chirality operator is suggestive of how to introduce the projector
operators of the corresponding projective modules on this space.
