We present the first grating-resolution X-ray spectra of the X-ray binary Cir X-1 , obtained with the High Energy Transmission Grating Spectrometer on Chandra . These reveal a rich set of lines from H-like and/or He-like Ne , Mg , Si , S and Fe detected with a high signal-to-noise ratio . The lines are broad ( \pm 2000 km s ^ { -1 } ) and show P Cygni profiles . The absorption components of the lines extend to low velocity , and they have about the same widths and strengths as the corresponding emission components . The widths of the X-ray P Cygni lines are comparable to that of the broad component of the strong , asymmetric H \alpha line from Cir X-1 , suggesting that the two phenomena may be related . We discuss outflow models and propose that the P Cygni profiles may arise in the moderate temperature ( \sim 5 \times 10 ^ { 6 } K ) region of the wind from an X-ray heated accretion disk . This basic picture strengthens the idea that the accretion disk in Cir X-1 is viewed in a relatively edge-on manner , and it suggests that Cir X-1 is the X-ray binary analog of a Broad Absorption Line quasar .