We present the first high-quality, moderate-resolution spectroscopy of Cygnus X-2 in the 0.4-12 keV energy range, obtained using the Broad Band X-Ray Telescope (BBXRT), part of the Astro-1 shuttle payload. These data enable us to resolve the physical width of the 6.7 keV Fe Kalpha feature in Cyg X-2 with an energy resolution a factor of 4 better than previous X-ray experiments. The feature is modeled well with a single broad Gaussian line with center energy E = 6.71(+0.23; -0.20), full width half-maximum 971(+505; -376) eV, and equivalent width 60 +/- 27 eV. There is also tentative evidence for Fe L line emission at 1 keV. A sensitive search for an iron edge feature in the 7-9 keV range results in an upper limit on the absorption depth of tau less-than-or-equal-to 0.15. There are three possible sites for the Fe Kalpha emission: the accretion disk, its corona, or the source itself. The last can be rejected as the continuum spectrum suggests that the central kT approximately 1.7 keV blackbody is Comptonized through tau approximately 20. Any line would thus be strongly downscattered, broadened, and lost. An origin in a corona covering the source and disk can also be ruled out as the observed broad line can be produced only in material with tau approximately 3, far in excess of the limits on the optical depth at the iron edge. A line from an optically thick corona out of the line of sight would be viewed only by reflection rather than transmission, so the photons would travel through tau approximately 1, also inconsistent with the lack of an iron edge. Reflection from the accretion disk itself, however, can produce a line of the observed energy, width, and equivalent width if the disk surface is highly ionized.