  We calculate the production cross-sections for the vector and pseudoscalar
bound states of two gluinos. It is shown that existing and future colliders
imply a realistic chance of observing gluinonium as a narrow peak in the
two-jet invariant mass spectrum. With an integrated luminosity of 0.2 fb$^{-1}$
at the Tevatron, and the high efficiency for tagging heavy quark jets at CDF,
one should be able to detect vector gluinonium for gluino masses up to about
170 GeV; or up to about 260 GeV for an upgraded Tevatron with a centre of mass
energy of 2 TeV and an integrated luminosity of 1 fb$^{-1}$. The significantly
higher energy and luminosity of LHC should allow pseudoscalar gluinonium to be
detected for gluino masses up to about 1500 GeV for an assumed luminosity of
200 fb$^{-1}$. These results are insensitive to the details of supersymmetry
models, provided that R-parity is conserved and the gluinos are lighter than
the squarks. In addition, gluinonium detection implies a relatively accurate
measure of the gluino mass, which is difficult to determine by other means.
