A general theory is presented for the problem of condensed-phase particle nucleation from gas-phase precursors via a sequence of reversible chemical reactions, where no supersaturated vapor exists. We consider a system in which nucleation is initiated by the reaction between an "initiating species" and a "growth species." Subsequent steps in cluster growth involve reversible reactions between a cluster and the growth species, producing a larger cluster and a volatile byproduct, which may be considered a "suppressing species." Following the mathematical formalism of homogeneous nucleation theory, a steady-state nucleation rate is derived in the form of a summation over discrete cluster sizes. The resulting nucleation rate is linearly proportional to the product of the concentrations of the initiating species and the growth species, while the ratio of the concentrations of the growth species to the suppressing species, relative to a suitably defined equilibrium value, is seen to play a similar role as the vapor saturation ratio in homogeneous nucleation.