We report on the discovery of an isolated, compact HII region in the Virgo cluster. The object is located in the diffuse outer halo of NGC 4388, or could possibly be in intracluster space. Star formation can thus take place far outside the main star forming regions of galaxies. This object is powered by a small starburst with an estimated mass of $sim 400msun$ and age of $sim 3myr$. From a total sample of 17 HII region candidates, the present rate of isolated star formation estimated in our Virgo field is small, $sim 10^{-6} Msun arcmin}^{-2} yr^{-1}$. However, this mode of star formation might have been more important at higher redshifts and be responsible for a fraction of the observed intracluster stars and total cluster metal production. This object is relevant also for distance determinations with the planetary nebula luminosity function from emission line surveys, for high-velocity clouds and the in situ origin of B stars in the Galactic halo, and for local enrichment of the intracluster gas by Type II supernovae.
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