  The trimer resonating valence bond (tRVB) state consisting of an equal-weight
superposition of trimer coverings on a square lattice is proposed. A model
Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact
ground state is written. The state is shown to have $9^g$ topological
degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation
functions show exponential behavior with a very short correlation length
consistent with the gapped spectrum. The classical problem of the degeneracy of
trimer configurations is investigated by the transfer matrix method.
