  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 $\sim 400\msun$ and age of $\sim
3\myr$. 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.
