We propose a chiral Fabry-Perot cavity in which only the cavity modes in almost pure spin (circular polarization) states lase in the presence of gain. In absence of imposed nonreciprocal environments and time-reversal symmetry breaking of emitter states to favor the emission of circularly-polarized photons, only the resonance of modes with a specific spin orientation remains in the cavity. We demonstrate a prototype of the cavity using distributed Bragg reflectors and cholesteric liquid crystals. This reciprocal cavity may provide a method to control the angular momentum state of emitters based on stimulated emissions.