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 L-FIR = 1.4 x 10(13) L-circle dot, and is lensed by a massive group of galaxies into at least four images with a total magnification of mu = 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 described well by warm, moderate-density gas with T-kin = 86-235 K and n(H2) = (1.1-3.5) x 10(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 T-kin similar to 200 K, n(H2) similar to 10(5) cm(-3) are also consistent with these data. Higher signal-to-noise measurements of the J(up) >= 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.