Moderate-resolution, near-IR spectroscopy of MS 1512-cB58 is presented, obtained during commissioning of the near-infrared spectrometer (NIRSPEC) on the Keck II telescope. The strong lensing of this z=2.72 galaxy by the foreground cluster MS 1512+36 makes it the best candidate for detailed study of the rest-frame optical properties of Lyman-break galaxies. In 80 minutes of on-source integration, we have detected Halpha, [N ii] lambdalambda6583, 6548, [O i] lambda6300, He i lambda5876, [O iii] lambdalambda5007, 4959, Hbeta, Hgamma, [O ii] lambda3727, and a strong continuum signal in the range of 1.29-2.46 µm. A redshift of z=2.7290+/-0.0007 is inferred from the emission lines, in contrast to the z=2.7233 calculated from UV observations of interstellar absorption lines. Using the Balmer line ratios, we find an extinction of E(B-V) = 0.27. Using the line strengths, we infer a star formation rate (SFR) of 620+/-18 M middle dot in circle yr-1 (H0=75, q0=0.1, and Lambda=0), which is a factor of 2 higher than that measured from narrowband imaging observations of the galaxy but is a factor of almost 4 lower than the SFR inferred from the UV continuum luminosity. The width of the Balmer lines yields a mass of Mvir=1.2x1010 M middle dot in circle. We find that the oxygen abundance is 13 solar, in good agreement with other estimates of the metallicity. However, we infer a high nitrogen abundance, which may argue for the presence of an older stellar population.