If, as argued by some, the cores of most galaxies contain supermassive black holes, galaxy-galaxy collisions could lead to their coalescence and a consequent emission of gravitational radiation. For holes with masses $\ensuremath{\ge}{10}^{6}{M}_{0}$, the amplitude of this radiation should be sufficiently large (metric perturbation \ensuremath{\sim}${10}^{\ensuremath{-}18}$-${10}^{\ensuremath{-}17}$) as to be detectable at the present horizon distance ${\mathcal{R}}_{H}\ensuremath{\sim}{10}^{10}$ light years using current technology. It is shown here that there is solid evidence indicating that galaxy collisions could have been sufficiently frequent at early times (redshifts $z\ensuremath{\sim}2\ensuremath{-}3$) to lead to a rate of potentially observable events as short as one every \ensuremath{\sim}1-100 yr.