  We analyze features of the Fe K spectrum of the high-mass X-ray binary Cygnus
X-3. The spectrum was obtained with the Chandra High Energy Transmission
Grating Spectrometer in the third diffraction order. The increased energy
resolution of the third order enables us to fully resolve the Fe XXV He{\alpha}
complex and the Fe XXVI Ly{\alpha} lines. The emission-line spectrum shows the
expected features of photoionization equilibrium, excited in the dense stellar
wind of the companion star. We detect discrete emission from inner-shell
transitions, in addition to absorption likely due to multiple unresolved
transitions in lower ionization states. The emission-line intensity ratios
observed in the range of the spectrum occupied by the Fe XXV n = 1-2 forbidden
and intercombination lines suggest that there is a substantial contribution
from resonantly scattered inner-shell emission from the Li- and Be-like
ionization states. The Fe XXV forbidden and intercombination lines arise in the
ionization zone closest to the compact object, and since they are not subject
to radiative-transfer effects, we can use them in principle to constrain the
radial velocity amplitude of the compact object. We infer that the results
indicate a compact object mass of the order of the mass of the Wolf-Rayet
companion star, but we note that the presence of resonantly scattered radiation
from Li-like ions may complicate the interpretation of the He-like emission
spectrum, and specifically of the radial velocity curve of the Fe XXV forbidden
line.
