We present new optical and infrared (IR) observations of Cir X-1 taken near apastron. Both sets of spectra show asymmetric emission lines. Archival optical observations show that an asymmetric Ha emission line has been in evidence for the past 20 years, although the shape of the line has changed significantly. We present an eccentric (e similar to 0.7-0.9) low-mass binary model, where the system consists of a neutron star orbiting around a (sub)giant companion star of 3-5 M. We suggest that the broad components of the emission lines arise in a high-velocity, optically thick flow near the neutron star, while the narrow components of the optical and the IR lines arise near the companion star and a heated ejecta shell surrounding the binary respectively. In this model, the velocity of the narrow component reflects the space velocity of the binary; the implied radial velocity (+430 km s(-1) after correcting for Galactic rotation) is the highest velocity known for an X-ray binary.