Two-tier networks, comprising a conventional cellular network overlaid with shorter range hotspots (e.g. femtocells, distributed antennas, or wired relays), offer an economically viable way to improve cellular system capacity. The capacity-limiting factor in such networks is interference. The cross-tier interference between macrocells and femtocells can suffocate the capacity due to the near-far problem, so in practice hotspots should use a different frequency channel than the potentially nearby high-power macrocell users. Centralized or coordinated frequency planning, which is difficult and inefficient even in conventional cellular networks, is all but impossible in a two-tier network. This paper proposes and analyzes an optimum decentralized spectrum allocation policy for two-tier networks that employ frequency division multiple access (including OFDMA). The proposed allocation is optimal in terms of Area Spectral Efficiency (ASE), and is subjected to a sensible Quality of Service (QoS) requirement, which guarantees that both macrocell and femtocell users attain at least a prescribed data rate. Results show the dependence of this allocation on the QoS requirement, hotspot density and the co-channel interference from the macrocell and surrounding femtocells. Design interpretations of this result are provided.