  The edge currents of two dimensional topological chiral superconductors with
nonzero Cooper pair angular momentum---e.g., chiral $p$-, $d$-, and $f$-wave
superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau
calculations are used to show that in the continuum limit, \emph{only} chiral
$p$-wave states have a nonzero edge current. Outside this limit, when lattice
effects become important, edge currents in non-$p$-wave superconductors are
comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a
simple criterion is derived for when edge currents vanish for non-$p$-wave
chiral superconductivity on a lattice. The implications of our results for
putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.
