  We report on the redshift measurement and CO line excitation of HERMES
J105751.1+573027 (HLSW-01), a strongly lensed submillimeter galaxy discovered
in Herschel/SPIRE observations as part of the Herschel Multi-tiered
Extragalactic Survey (HerMES). HLSW-01 is an ultra-luminous galaxy with an
intrinsic far-infrared luminosity of 1.4x10^(13) solar luminosities, and is
lensed by a massive group of galaxies into at least four images with a total
magnification of 10.9+/-0.7. With the 100 GHz instantaneous bandwidth of the
Z-Spec instrument on the Caltech Submillimeter Observatory, we robustly
identify a redshift of z=2.958+/-0.007 for this source, using the simultaneous
detection of four CO emission lines (J = 7-6, J = 8-7, J = 9-8, and J = 10-9).
Combining the measured line fluxes for these high-J transitions with the J =
1-0, J = 3-2 and J = 5-4 line fluxes measured with the Green Bank Telescope,
the Combined Array for Research in Millimeter Astronomy, and the Plateau de
Bure Interferometer, respectively, we model the physical properties of the
molecular gas in this galaxy. We find that the full CO spectral line energy
distribution is well described by warm, moderate-density gas with Tkin = 86-235
K and n(H2) = (1.1-3.5)x10^3 cm^(-3). However, it is possible that the
highest-J transitions are tracing a small fraction of very dense gas in
molecular cloud cores, and two-component models that include a warm/dense
molecular gas phase with Tkin ~ 200 K, n(H2) ~ 10^5 cm^(-3) are also consistent
with these data. Higher signal-to-noise measurements of the J(upper) > 7
transitions with high spectral resolution, combined with high spatial
resolution CO maps, are needed to improve our understanding of the gas
excitation, morphology, and dynamics of this interesting high-redshift galaxy.
