We present Hubble Space Telescope images of star-forming galaxies at redshifts z > 3 . These galaxies have been selected using ground–based images and color criteria sensitive to the presence of a Lyman discontinuity in the otherwise flat ( in f _ { \nu } units ) UV spectral energy distribution 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 , which probe the rest-frame UV between 1400 and 1900 Å , show that the morphologies of the z > 3 galaxies are generally compact and exhibit a relatively high degree of spherical symmetry , although we find a few cases of more diffuse light profiles and several cases where the objects are comprised of multiple compact structures . Overall , the dispersion of morphological properties is relatively narrow , in contrast to the variety found in star-forming galaxies at intermediate redshifts ( z \sim 1 ) . The galaxies with compact morphology are typically characterized by a small but resolved “ core ” , approximately \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.7 arcsec in radius , or about 5 h _ { 50 } ^ { -1 } ( 8.5 h _ { 50 } ^ { -1 } ) 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 } ^ { -1 } ( 2.4 – 3.6 h _ { 50 } ^ { -1 } ) 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 . The morphological properties , space density , star-formation rates , masses , and early 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 their spheroidal components .