  The purple bronze Li$_{0.9}$Mo$_6$O$_{17}$ is of interest due to its
quasi-one-dimensional electronic structure and the possible Luttinger liquid
behavior resulting from it. For sufficiently low temperatures, it is a
superconductor with a pairing symmetry that is still to be determined. To shed
light on this issue, we analyze a minimal Hubbard model for this material
involving four molybdenum orbitals per unit cell near quarter filling, using
asymptotically exact perturbative renormalization group methods. We find that
spin triplet odd-parity superconductivity is the dominant instability.
Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces
enhance certain second-order processes, which play crucial roles in determining
the structure of the pairing gap. Notably, we find that the gap has accidental
nodes, i.e. it has more sign changes than required by the point-group symmetry.
