  We calculate the expected number of multiply-imaged galaxies in the Hubble
Deep Field (HDF), using photometric redshift information for galaxies with m_I
< 27 that were detected in all four HDF passbands. A comparison of these
expectations with the observed number of strongly lensed galaxies constrains
the current value of Omega_m-Omega_Lambda, where Omega_m is the mean mass
density of the universe and Omega_Lambda is the normalized cosmological
constant. Based on current estimates of the HDF luminosity function and
associated uncertainties in individual parameters, our 95% confidence lower
limit on Omega_m-Omega_Lambda ranges between -0.44, if there are no strongly
lensed galaxies in the HDF, and -0.73, if there are two strongly lensed
galaxies in the HDF. If the only lensed galaxy in the HDF is the one presently
viable candidate, then, in a flat universe (Omega_m+Omega_Lambda=1),
Omega_Lambda < 0.79 (95% C.L.). These limits are compatible with estimates
based on high-redshift supernovae and with previous limits based on
gravitational lensing.
