VIRGOHI 21 is an H I source detected in the Virgo Cluster survey of Davies et al. that has a neutral hydrogen mass of 108 M and a velocity width of ?V20 = 220 km s-1. From the Tully-Fisher relation, a galaxy with this velocity width would be expected to be 12 mag or brighter; however, deep CCD imaging has failed to turn up a counterpart down to a surface brightness level of 27.5 B mag arcsec-2. The H I observations show that it is extended over at least 16 kpc, which, if the system is bound, gives it a minimum dynamical mass of ~1011 M and a mass-to-light ratio of Mdyn/LB > 500 M/L. If it is tidal debris, then the putative parents have vanished; the remaining viable explanation is that VIRGOHI 21 is a dark halo that does not contain the expected bright galaxy. This object was found because of the low column density limit of our survey, a limit much lower than that achieved by all sky H I surveys such as those carried out at Parkes and Jodrell Bank. Further such sensitive surveys might turn up a significant number of the dark matter halos predicted by galaxy formation models.