  We combine data from the extremely deep Hubble Space Telescope $U$ (F300W)
image obtained using WFPC2 as part of the parallel observations of the Hubble
Ultra Deep Field campaign, with $BVi$ images from the Great Observatories
Origins Deep Survey (GOODS) to identify a sample of Lyman break galaxies in the
redshift range $2.0 \lesssim z \lesssim 3.5$. We use recent stellar population
synthesis models with a wide variety of ages, metallicities, redshifts, and
dust content, and a detailed representation of the \HI cosmic opacity as a
function of redshift to model the colors of galaxies in our combination of
WFPC2/ACS filters. Using these models, we derive improved color selection
criteria that provide a clean selection of relatively unobscured, star forming
galaxies in this redshift range. Our WFPC2/F300W image is the deepest image
ever obtained at that wavelength. The $10\sigma$ limiting magnitude measured
over 0.2 arcsec$^2$ is 27.5 magnitudes in the WFPC2/F300W image, about 0.5
magnitudes deeper than the F300W image in the Hubble Deep Field (HDF)-N. This
extra depth relative to the HDFs allows us to directly probe the luminosity
function about 0.5 magnitudes deeper than the depth accessible with the HDF
data along an independent line of sight. Our sample of star-forming galaxies
with $2.0 \lesssim z \lesssim 3.5$ includes 125 objects, the majority of which
show clumpy morphologies. We measure a star formation rate density of 0.18
  $M_\odot \rm yr^{-1} Mpc^{-3}$, marginally higher than the value measured for
the Hubble Deep Fields.
