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 $\mathbf K$- and $\mathbf K^\prime$-valleys, which carry the opposite topological charges, $\pm1$, and are described by a two-dimensional $E^{\prime}$ 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

9 pages, 7 figures