  We present HST images of star-forming galaxies at redshifts z>3. These
galaxies have been color selected for having a Lyman discontinuity in the
otherwise flat (in f_\nu units) UV spectra of unreddened star formation. The
spectroscopic confirmation of these z>3 galaxies is reported in a companion
paper (Steidel et al. 1996). The HST images probe the rest-frame UV at
1400--1900 Ang and show that the morphologies of the z>3 galaxies are generally
compact, although we find a few cases of more diffuse light profiles and
objects comprised of multiple compact structures. Overall, the dispersion of
morphologies is relatively narrow, in contrast to the variety found in
star-forming galaxies at intermediate redshifts (z~1). The galaxies with
compact morphology are typically characterized by a small but resolved
``core'', approximately <0.7 arcsec in radius, or about 5 h_50 (8.5 h_50) kpc
with q_0=0.5 (0.05), and half-light radii of 0.2--0.3 arcsec, or 1.4--2.1 h_50
(2.4--3.6 h_50) kpc. These sizes and scale lengths are similar to those of
present-day bulges or intermediate-luminosity spheroids. The ``cores'' are
often surrounded by lower surface-brightness nebulosities, generally
asymmetrically distributed. The minority of more diffuse galaxies do not
possess this core, and an exponential function provides a very good fit to
their light profiles. In contrast to highly elongated or irregular structures,
such as ``chain galaxies'', that are found at $z \sim 1$, the z>3 galaxies are
characterized by a relatively high degree of spherical symmetry. Morphology,
space density, star-formation rates, masses, and epoch of the star-formation
phase all support the hypothesis that we have identified the progenitors of
present-day luminous galaxies at the epoch when they were forming the stars of
