One of the classical problems facing radio astronomers is to acquire optical follow-up material for radio source surveys. Often it may take years of work to obtain the optical identifications and redshifts needed to find the optical counterparts of the radio sources and to determine their redshift and luminosity. The availability of the Hubble Deep Field (Williams et al. 1996) with its aggressive ground based optical follow-up as well as auxiliary space based observations in other wavelength bands offers a unique opportunity to investigate the nature of the radio emission from normal or nearly normal galaxies at cosmologically interesting distances. In this paper we report on preliminary results of Very Large Array observations of the radio counterparts of galaxies in the Hubble Deep Field.