The triatomic hydrogen cation solvated by rare gases, Rg(n)H(3)(+), n=1-5, Rg=He, Ne, Ar, Kr, Xe, is investigated by density functional theory. The results indicate that while the first solvent atom distorts and destabilizes the H-3(+) center, the ion is restabilized by additional solvation. For the n=3 species, the symmetric D-3h structure is the global minimum for all rare gases except Xe; the n=4,5 solvent atoms are placed on the C-3 axis of the molecule. The computed potential energy surface of the isomerization reaction Rg(n)H(3)(+)--> HRg(2)H(+)Rg(n-2), n=2-4, provides insight into the possible H-3(+) formation and destruction mechanisms in rare gas matrices. As expected, solid neon is the most suitable medium for H-3(+) studies, with its stabilization becoming progressively more difficult in the heavier rare gas solids.