We observed the Galactic black hole Cygnus X-1 with the Chandra High Energy Transmission Grating Spectrometer for 30 kiloseconds on 2001 January 4 . The source was in an intermediate state , with a flux that was approximately twice that commonly observed in its persistent low/hard state . Our best-fit model for the X-ray spectrum includes narrow Gaussian emission line ( E = 6.415 \pm 0.007 keV , FWHM = 80 ^ { +28 } _ { -19 } eV , W = 16 ^ { +3 } _ { -2 } eV ) and broad line ( E= 5.82 ^ { +0.06 } _ { -0.07 } keV , FWHM = 1.9 ^ { +0.5 } _ { -0.3 } keV , W = 140 ^ { +70 } _ { -40 } eV ) components , and a smeared edge at 7.3 \pm 0.2 keV ( \tau \sim 1.0 ) . The broad line profile is not as strongly skewed as those observed in some Seyfert galaxies . We interpret these features in terms of an accretion disk with irradiation of the inner disk producing a broad Fe K \alpha emission line and edge , and irradiation of the outer disk producing a narrow Fe K \alpha emission line . The broad line is likely shaped predominantly by Doppler shifts and gravitational effects , and to a lesser degree by Compton scattering due to reflection . We discuss the underlying continuum X-ray spectrum and these line features in the context of diagnosing the accretion flow geometry in Cygnus X-1 and other Galactic black holes .