We report spectroscopic observations of the earthshine reflected from the Moon. By applying our well-developed photometry methodology to spectroscopy, we are able to precisely determine the Earth's reflectance and its variation as a function of wavelength through a single night as the Earth rotates. These data imply that planned regular monitoring of earthshine spectra will yield valuable new inputs for climate models, which would be complementary to those from the more standard broadband measurements of satellite platforms. For our single night of reported observations, we find that Earth's albedo decreases sharply with wavelength from 500 to 600 nm, while being almost flat from 600 to 900 nm. The mean spectroscopic albedo over the visible is consistent with simultaneous broadband photometric measurements. Unlike previous reports, we find no evidence for either an appreciable ``red'' or ``vegetation'' edge in the Earth's spectral albedo, or for changes in this spectral region (700-740 nm) over the 40° of Earth's rotation covered by our observations. Whether or not the absence of a vegetation signature in disk-integrated observations of the Earth is a common feature awaits the analysis of more earthshine data and simultaneous satellite cloud maps at several seasons. If our result is confirmed, it would limit efforts to use the red edge as a probe for Earth-like extrasolar planets. Water vapor and molecular oxygen signals in the visible earthshine, and carbon dioxide and methane in the near-infrared, are more likely to be powerful probes.