We analyse the classical and quantum properties of the nonintegrable trimer problem. The Hamiltonian exhibits permutation symmetry. A single parameter tunes the distance of the system from the integrable dimer. There exist classical trajectories - both regular and chaotic - which are not invariant under permutation. We numerically diagonalize the quantum Hamiltonian and investigate properties of pairs of tunnelling eigenstates, and compare to the corresponding classical phase-space properties. Tunnelling states survive avoided crossings with other states, and continue to exist as long as the classical phase space supports regular islands. We relate these findings to the problem of quantum breathers and single-bond excitations in molecules.