Dedicated monitoring of the transient X-ray pulsar XTE J1543-568 during the
first year after its discovery has revealed the unambiguous detection of a
binary orbit. The orbital period is days, and the 75.56 +/- 0.25 projected
semimajor axis is 353 +/- 8 lt-s. The mass function and position in the pu
lse period versus orbital period diagram are consistent with XTE J1543-568
being a Be X-ray binary. The eccentricity of less than 0.03 (2 sigma) is am
ong the lowest for the 12 Be X-ray binaries whose orbits have now been meas
ured. This confirms the suspicion that small kick velocities of neutron sta
rs during supernovae are more common than expected. The distance is estimat
ed to be larger than 10 kpc and the luminosity at least 10(37) ergs s(-1).