  We have analyzed the kinematical parameters of Cir X-1 to constrain the
nature of its companion star, the eccentricity of the binary and the
pre-supernova parameter space. We argue that the companion is most likely to be
a low-mass (< 2.0 M_sun) unevolved star and that the eccentricity of the orbit
is 0.94 +/- 0.04. We have evaluated the dynamical effects of the supernova
explosion and we find it must have been asymmetric. On average, we find that a
kick of 740 km/s is needed to account for the recently measured radial velocity
of +430 km/s (Johnston, Fender & Wu) for this extreme system. The corresponding
minimum kick velocity is 500 km/s. This is the largest kick needed to explain
the motion of any observed binary system. If Cir X-1 is associated with the
supernova remnant G321.9-0.3 then we find a limiting minimum age of this
remnant of 60000 yr. Furthermore, we predict that the companion star has lost
10% of its mass as a result of stripping and ablation from the impact of the
supernova shell shortly after the explosion.
