Changes in the one- and two-particle densities arising from Coulomb correlation have been examined, in detail, for the ground state of H-3(+). This electron deficient system was described in its equilateral triangular conformation by a wave function which recovered approximately 99% of the correlation energy. Contour diagrams are presented for densities evaluated in the molecular plane and also in a plane perpendicular to the molecule. For the two-particle distribution, correlation effects are highlighted in different regions of the system by considering a series of fixed positions for a "test" or "reference" electron. In addition, for each location of the test particle, planar Coulomb holes are determined which emphasize the relative importance of the radial and angular components of correlation. Contrary to an earlier study, it is demonstrated that Coulomb correlation reduces the density within the H-3(+) nuclear triangle. The present findings are compared with a similar analysis for the H-2 molecule in position (real) space, already reported.