We report the discovery of a large H. cloud in the central regions of the Virgo cluster. It is 110 x 25 kpc in size and contains 3.4 x 10(8) M-circle dot of H I. The morphology and kinematics of this cloud strongly suggest that it consists of H I. removed from the galaxy NGC 4388 by ram-pressure stripping. It is more likely the result of an interaction of the ISM of NGC 4388 with the hot halo of the M86 group and not with the ICM centred on M87. The large extent of the plume suggests that gas stripped from cluster galaxies can remain neutral for at least 10(8) yr. Locally, the column density is well above 10(20) cm(-2), suggesting that the, intra-cluster H II regions known to exist in Virgo may have formed from gas stripped from cluster galaxies. The existence of the H I plume suggests that stripping of infalling spirals to the enrichment of the ICM. The H I object in the Virgo cluster recently reported by Minchin et al. (2005, ApJ, 622, L21) may have a similar origin and may therefore not be a "dark galaxy".