The spaser, a quantum amplifier of surface plasmons by stimulated emission of radiation, is recognized as a coherent light source capable of confining optical fields at subwavelength scale. The control over the directionality of spasing has not been addressed so far, especially for a single-particle spasing nanocavity where optical feedback is solely provided by a plasmon resonance. In this work we numerically examine an asymmetric spaser - a resonant system comprising a dielectric core capped by a metal semishell. The proposed spaser emits unidirectionally along the axis of the semishell; this directionality depends neither on the incident polarization nor on the incident angle of the pump. The spasing efficiency of the semishell-capped resonator is one order of magnitude higher than that in the closed core-shell counterpart. Our calculations indicate that symmetry breaking can serve as a route to create unidirectional, highly intense, single-particle, coherent light sources at subwavelength scale.