We present spectroscopy from the Keck telescope of three sets of objec
ts in the Hubble Deep Field (HDF) that have lens-like morphologies. In
the case of J123641+621204, which is composed of four objects with si
milar colors and a mean separation of less than or similar to 0.'' 8,
we find at least two distinct components at redshifts of z = 3.209 and
z = 3.220 that are separated by 0.'' 5 spatially. Each of these compo
nents has narrow Ly alpha emission and possibly N V emission and Si IV
and C IV in absorption or with a P Cygni profile. The second case is
J123652+621227, which has an arclike feature offset by 1.'' 8 to the s
outhwest of a red elliptical-like galaxy and a ''counterimage'' offset
1.'' 4 on the opposite side. We tentatively find a single line at 530
1 Angstrom at the spatial position of the counterimage and no correspo
nding emission line at the position of the are. The colors of the coun
terimage are consistent with the identification of this line as Ly alp
ha at z = 3.36. The colors of the are 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 can
didate (J123656+621221), which is a blue are offset by 0.'' 9 from a r
ed, elliptical-like galaxy, our spectroscopy does not clearly resolve
the system spatially, which complicates the interpretation of the spec
trum. We discuss possible identifications of a number of absorption fe
atures and a very tentative detection of a pair of emission lines at 5
650 Angstrom and 5664 Angstrom, and we 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 ver
y 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 and tends to favo
r models in which very faint galaxies are at fairly modest redshifts.