In the giant impact theory for lunar origin, the Moon forms from material ejected by the impact into an Earth-orbiting disk. Here we report the initial results from a silicate melt-vapor equilibrium chemistry model for such impact-generated planetary debris disks. In order to simulate the chemical behavior of a two-phase (melt+vapor) disk, we calculate the temperature-dependent pressure and chemical composition of vapor in equilibrium with molten silicate from 2000 to 4000 K. We consider the elements O, Na, K, Fe, Si, Mg, Ca, Al, Ti, and Zn for a range of bulk silicate compositions (Earth, Moon, Mars, eucrite parent body, angrites, and ureilites). In general, the disk atmosphere is dominated by Na, Zn, and O2 at lower temperatures (< 3000 K) and SiO, O2, and O at higher temperatures. The high-temperature chemistry is consistent for any silicate melt composition, and we thus expect abundant SiO, O2, and O to be a common feature of hot, impact-generated debris disks. In addition, the saturated silicate vapor is highly oxidizing, with oxygen fugacity (fO2) values (and hence H2O/H2 and CO2/CO ratios) several orders of magnitude higher than those in a solar-composition gas. High fO2 values in the disk atmosphere are found for any silicate composition because oxygen is the most abundant element in rock. We thus expect high oxygen fugacity to be a ubiquitous feature of any silicate melt-vapor disk produced via collisions between rocky planets.