  We present results from the first robust investigation of galaxy morphology
as a function of environment at z>1.5. Our study is motivated by the fact that
star-forming galaxies contained within a protocluster at z=2.3 in the HS1700+64
field have significantly older ages and larger stellar masses on average than
those at similar redshifts but more typical environmental densities. In the
analysis of HST/ACS images, we apply non-parametric statistics to characterize
the rest-frame UV morphologies of a sample of 85 UV-selected star-forming
galaxies at z=1.7-2.9, 22 of which are contained in the protocluster. The
remaining 63 control-sample galaxies are not in the protocluster but have a
similar mean redshift of <z>~2.3. We find no environmental dependence for the
distributions of morphological properties. Combining the measured morphologies
with the results of population synthesis modeling, we find only weak
correlations, if any, between morphological and stellar population properties
such as stellar mass, age, extinction and star-formation rate. Given the
incomplete census of the protocluster galaxy population, and the lack of
correlation between rest-frame UV morphology and star-formation history at z~2
within our sample, the absence of environmental trends in the distribution of
morphological properties is not surprising. Additionally, using a larger sample
of photometric candidates, we compare morphological distributions for 282
UV-selected and 43 near-IR-selected galaxies. While the difference in the
degree of nebulosity between the two samples appears to be a byproduct of the
fainter average rest-frame UV surface brightness of the near-IR-selected
galaxies, we find that, among the lowest surface brightness galaxies, the
near-IR-selected objects have significantly smaller angular sizes (abridged).
