  We present spectroscopy from the Keck telescope of three sets of objects in
the Hubble Deep Field which have lens-like morphologies. In the case of
J123641+621204, which is composed of four objects with similar colors and a
mean separation of <= 0.8", we find at least two distinct components at
redshifts of z=3.209 and z=3.220 which are separated by 0.5" spatially. Each of
these components has narrow Ly-alpha emission, and possibly NV emission and
SiIV and CIV in absorption or with a P-Cygni profile. The second case is
J123652+621227, which has an arc-like feature offset by 1.8" to the southwest
of a red elliptical-like galaxy, and a ``counterimage'' offset 1.4" on the
opposite side. We tentatively find a single line at 5301 AA at the spatial
position of the counterimage, and no corresponding emission line at the
position of the arc. The colors of the counterimage are consistent with the
identification of this line as Ly-alpha at z=3.36. The colors of the arc are
different than those of the counterimage, and thus both the colors and spectra
indicate that this object is unlikely to be a gravitational lens. For a third
lensing candidate (J123656+621221), which is a blue arc offset by 0.9" from a
red, elliptical-like galaxy, our spectroscopy does not clearly resolve the
system spatially, complicating the interpretation of the spectrum. We discuss
possible identifications of features in the spectrum, and find that
gravitational lensing remains a possibility in this case. We conclude that the
frequency of strong gravitational lensing by galaxies in the HDF appears to be
very low. This result is difficult to reconcile with the introduction of a
cosmological constant to account for the large number of faint blue galaxies
via a large volume element at high redshift.
