We theoretically introduce a topological spaser, which consists of a hexagonal array of plasmonic metal nanoshells containing an achiral gain medium in their cores. Such a spaser can generate two mutually time-reversed chiral surface plasmon modes in the K and K^{'} valleys, which carry the opposite topological charges, ±1, and are described by a two-dimensional E^{'} representation of the D_{3h} point symmetry group. Due to the mode competition, this spaser exhibits a bistability: only one of these two modes generates, which is a spontaneous symmetry breaking. Such a spaser can be used for an ultrafast all-optical memory and information processing, and biomedical detection and sensing with chirality resolution.