We present the results of a detailed study of the interstellar medium of MS 1512-cB58, an L* Lyman break galaxy at z = 2.7276, based on new spectral observations obtained with the Echelle Spectrograph and Imager on the Keck II telescope at 58 km/s resolution. We focus in particular on the chemical abundances and kinematics of the interstellar gas and our main findings are as follows. Even at this relatively early epoch, the ISM of this galaxy is already highly enriched in elements released by Type II supernovae; the abundances of O, Mg, Si, P, and S are all about 2/5 of their solar values. In contrast, N and the Fe-peak elements Mn, Fe, and Ni are underabundant by a factor of about 3. Based on current ideas of stellar nucleosynthesis, these results can be understood if most of the metal enrichment in cB58 has taken place within the last 300 million years, the timescale for the release of N from intermediate mass stars. cB58 appears to be an example of a galaxy in the process of converting its gas into stars on a few dynamical timescales; quite possibly we are witnessing the formation of a galactic bulge or an elliptical galaxy. The energetic star formation activity has stirred the interstellar medium to high velocities of up to 1000 km/s. The net effect is a bulk outflow of the ISM at a speed of 255 km/s and at a rate which exceeds the star formation rate. It is unclear whether this gas will be lost or retained by the galaxy. We point out that the chemical and kinematic properties of cB58 are markedly different from those of most damped Lyman alpha systems at the same redshift., 38 pages, LaTeX, 9 Postscript Figures. Accepted for publication in the Astrophysical Journal. Sections 3.3 and 5.3 expanded, and two additional figures included, following referee's report