The Pyxis globular cluster is a recently discovered globular cluster that lies in the outer halo (R_{gc} ~ 40 kpc) of the Milky Way. Pyxis lies along one of the proposed orbital planes of the Large Magellanic Cloud (LMC), and it has been proposed to be a detached LMC globular cluster captured by the Milky Way. We present the first measurement of the radial velocity of the Pyxis globular cluster based on spectra of six Pyxis giant stars. The mean heliocentric radial velocity is ~ 36 km/sec, and the corresponding velocity of Pyxis with respect to a stationary observer at the position of the Sun is ~ -191 km/sec. This radial velocity is a large enough fraction of the clusters expected total space velocity, assuming that it is bound to the Milky Way, that it allows strict limits to be placed on the range of permissible transverse velocities that Pyxis could have in the case that it still shares or nearly shares an orbital pole with the LMC. We can rule out that Pyxis is on a near circular orbit if it is Magellanic debris, but we cannot rule out an eccentric orbit associated with the LMC. We have calculated the range of allowed proper motions for the Pyxis globular cluster that result in the cluster having an orbital pole within 15 degrees of the present orbital pole of the LMC and that are consistent with our measured radial velocity, but verification of the tidal capture hypothesis must await proper motion measurement from the Space Interferometry Mission or HST. A spectroscopic metallicity estimate of [Fe/H] = -1.4 +/- 0.1 is determined for Pyxis from several spectra of its brightest giant; this is consistent with photometric determinations of the cluster metallicity from isochrone fitting.
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