  We show that in a two-dimensional electron gas with an annular Fermi surface,
long-range Coulomb interactions can lead to unconventional superconductivity by
the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the
inner and outer Fermi surfaces are close to each other. The most prevalent
state has chiral $p$-wave symmetry, but $d$-wave and extended $s$-wave pairing
are also possible. We discuss these results in the context of rhombohedral
trilayer graphene, where superconductivity was recently discovered in regimes
where the normal state has an annular Fermi surface. Using realistic
parameters, our mechanism can account for the order of magnitude of $T_c$, as
well as its trends as a function of electron density and perpendicular
displacement field. Moreover, it naturally explains some of the outstanding
puzzles in this material, that include the weak temperature dependence of the
resistivity above $T_c$, and the proximity of spin singlet superconductivity to
the ferromagnetic phase.
