We report the discovery of a ~500 kpc HI extension southwest of the Virgo Cluster HI-rich pair NGC 4532/DDO 137, detected as part of the Arecibo Legacy Fast ALFA (ALFALFA) Survey. The feature is the longest and most massive HI tail structure so far found in the Virgo Cluster and, at 1.8 Mpc from M87, the most distant from the main concentration of the intracluster medium. The structure is spatially and spectrally separated into two ridges and is defined by diffuse emission and discrete clumps of mass 2.5 - 6.8 x 10**7 solar masses. All emission is blue-shifted with respect to the NGC 4532/DDO 137 pair emission. Including diffuse emission, the structure has a total mass of up to 7 x 10**8 solar masses, equivalent to ~10% of the systems HI mass. Optical R-band imaging finds no counterparts to a level of 26.5 mag arcsec**-2. The characteristics of the structure appear most consistent with a tidal origin.
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