  We study D-branes that preserve a diagonal SL(2) affine Lie algebra in string
theory on AdS_3. We find three classes of solutions, corresponding to the
following representations of SL(2): (1) degenerate, finite dimensional
representations with half integer spin, (2) principal continuous series, (3)
principal discrete series. We solve the bootstrap equations for the vacuum wave
functions and discuss the corresponding open string spectrum. We argue that
from the point of view of the AdS/CFT correspondence, the above D-branes
introduce boundaries with conformal boundary conditions into the two
dimensional spacetime. Open string vertex operators correspond to boundary
perturbations. We also comment on the geometric interpretation of the branes.
