Dicke's original thought experiment with two spins (two-level atoms) coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to many spins as a way to synthesize highly entangled states. We suggest a protocol in which we start with a direct product state of M atoms in the excited state and N atoms in the ground state, placed within a lossy cavity. A null observation for photon emission collapses the system onto a dark state which, remarkably, has resonating valence bond (RVB) character. We demonstrate this by taking advantage of the symmetry of the initial state under permutations of the M excited atoms and of the N unexcited atoms. Using angular momentum analysis, we reexpress the wavefunction of the dark state to illustrate its RVB character. We discuss two limiting cases in detail, with M = 1 (one excited atom) and M = N (equal number of excited and unexcited atoms). In the latter case, we show that the probability for null emission scales as N −1 making it possible to generate highly entangled RVB states of 20 spins or more.