Bose–Einstein condensation is a remarkable manifestation of quantum statistics and macroscopic quantum coherence. Superconductivity and superfluidity have their origin in Bose–Einstein condensation. Ultracold quantum gases have provided condensates close to the original ideas of Bose and Einstein, while condensation of polaritons and magnons has introduced novel concepts of non-equilibrium condensation. Here, we demonstrate a Bose–Einstein condensate of surface plasmon polaritons in lattice modes of a metal nanoparticle array. Interaction of the nanoscale-confined surface plasmons with a room-temperature bath of dye molecules enables thermalization and condensation in picoseconds. The ultrafast thermalization and condensation dynamics are revealed by an experiment that exploits thermalization under propagation and the open-cavity character of the system. A crossover from a Bose–Einstein condensate to usual lasing is realized by tailoring the band structure. This new condensate of surface plasmon lattice excitations has promise for future technologies due to its ultrafast, room-temperature and on-chip nature.