We observed the black hole candidate Cyg X-1 for 15 ks with the High-Energy Transmission Grating Spectrometer aboard the Chandra X-Ray Observatory. The source was observed during a period of intense flaring activity, so it was about a factor of 2.5 brighter than usual, with a 0.5-10 keV (1-24 Angstrom) luminosity of 1.6 x 10(37) ergs s(-1) (at a distance of 2.5 kpc). The spectrum of the source shows prominent absorption edges, some of which have a complicated substructure. We use the most recent results from laboratory measurements and calculations to model the observed substructure of the edges. From the model, we derive a total absorption column of (6.21 +/- 0.22) x 10(21) cm(-2). Furthermore, the results indicate that there are similar to 10%-25% abundance variations relative to solar values for neon, oxygen, and iron. The X-ray continuum is well described by a two-component model that is often adopted for black hole candidates: a soft multicolor disk component (with kT = 203 eV) and a hard power-law component (with a photon index of similar to2). Comparing the fit results to those of the hard and soft states, we conclude that the source was in a transitional state. Finally, the spectrum also shows the presence of faint emission lines, which could be attributed to highly ionized species.