We present model fits to the X-ray line spectrum of the well-known high-mass X-ray binary Cyg X-3. The primary observational data set is a spectrum taken with the Chandra X-ray Observatory High Energy Transmission Grating in 2006, though we compare it to all the other observations of this source taken so far by this instrument. We show that the density must be >= 10(12) cm(-3) in the region responsible for most of the emission. We discuss the influence of the dust scattering halo on the broadband spectrum, and we argue that dust scattering and extinction is not the most likely origin for the narrow feature seen near the Si K edge. We identify the features of a wind in the profiles of the strong resonance lines and show that the wind is more apparent in the lines from the lighter elements. We argue that this wind is most likely associated with the companion star. We show that the intensities of most lines can be fitted, crudely, by a single-component photoionized model. However, the iron K lines do not fit with this model. We show that the iron K line variability as a function of orbital phase is different from the lower-energy lines, which indicates that the lines arise in physically distinct regions. We discuss the interpretation of these results in the context of what is known about the system and similar systems.