The Near Earth Asteroid 4179 Toutatis will make a close approach to the Earth on Dec 12, 2012 at 6:40 am (UT) according to an ephemeris generated by JPL's HORIZONS website. A summary of the data in the ephemeris is given in the following table.
I loaded the orbital elements for Sep. 30, 2012 into Distant Suns and got the position indicated by the small white + for the time of close approach. The red marker shows the HORIZONS coordinates from the table above. The orbit may have been perturbed by the asteroid's proximity to the Earth. The perihelion longitude is ϖ=Ω+ω where Ω is the angle of the Ascending Node or the angular distance along the equator from the Vernal Equinox to the point where the orbit crosses the equator and ω is the argument of perihelion which is the angle from the equitorial plane to the asteroid's perihelion in the plane of its orbit. The asteroid's path is roughly parallel to the Ecliptic (the diagonal line through Pisces) but shows maximum deviation from it at the time of close approach. The apparent magnitude at close approach is given as 10.86 which means that one will need a telescope to see it.