We report on the initial results of a spectroscopic investigation of galaxies in the Hubble Deep Field which exhibit spectral discontinuities between the F450W and F300W passbands, indicative of the presence of the Lyman continuum break in the redshift range 2.4 < z < 3.4. We have employed color selection criteria similar to those we have used for selecting high redshift galaxy candidates from ground--based images. We find that, as for the ground--based color selection, the criteria are very successful in selecting high redshift objects. Of the 8 galaxies observed (selected from a list of 23 candidates with magnitudes equivalent to R <= 25.3, five have confirmed redshifts in the range 2.59 <= z <= 3.22, with the remaining 3 being indeterminate because of contamination from nearby brighter objects. As expected, the HST filter system is sensitive to a somewhat broader range of redshifts than our ground--based U_nGR filter system, and therefore the surveyed volume per unit area on the sky is correspondingly larger. The distribution of candidates on the plane of the sky is clearly non--uniform, consistent with the available ground--based data on the high redshift galaxies. Most Lyman break objects in the Hubble Deep Field exhibit a similar range of morphological properties to the z > 3 galaxies we have previously identified in other fields, characterized by very compact cores (some with multiple components) with half--light radii of 0.2-0.3 arcseconds, often surrounded by more diffuse and asymmetric ``halos''. A few of the brighter HDF Lyman break galaxies, however, have particularly unusual morphologies.