We report the discovery of four candidate intracluster globular clusters (IGCs) in a single deep HST ACS field of the Virgo Cluster. We show that each cluster is roughly spherical, has a magnitude near the peak of the Virgo globular cluster luminosity function, has a radial profile that is best fitted by a King model, and is surrounded by an excess of point sources that have the colors and magnitudes of cluster red giant stars. Despite the fact that two of our IGC candidates have integrated colors redder than the mean of the M87 globular cluster system, we propose that all of the objects are metal-poor, with [M/H]<-1. We show that the tidal radii of our intracluster globular clusters are all larger than the mean for Milky Way clusters and suggest that the clusters have undergone less tidal stress than their Galactic counterparts. Finally, we normalize our globular cluster observations to the luminosity of intracluster stars and derive a value of SN~6 for the specific frequency of Virgo intracluster globular clusters. We use these data to constrain the origins of Virgo's intracluster population and suggest that globular clusters in our intracluster field have a different origin than globular clusters in the vicinity of M87. In particular, we argue that dwarf elliptical galaxies may be an important source of intracluster stars.