Polaritons are quasiparticles arising from the strong coupling of electromagnetic waves in cavities and dipolar oscillations in a material medium. In this framework, localized surface plasmon in metallic nanoparticles defining optical nanocavities have attracted increasing interests in the past decade. This interest results from their sub-diffraction mode volume, which offers access to extremely high photonic densities by exploiting strong scattering cross sections. However, high absorption losses in metals have hindered the observation of collective coherent phenomena, such as condensation. In this work, we demonstrate the formation of a nonequilibrium room temperature plasmon-exciton-polariton condensate with a long-range spatial coherence, extending a hundred of microns, well over the excitation area, by coupling Frenkel excitons in organic molecules to a multipolar mode in a lattice of plasmonic nanoparticles. Time-resolved experiments evidence the picosecond dynamics of the condensate and a sizable blueshift, thus measuring for the first time the effect of polariton interactions in plasmonic cavities. Our results pave the way to the observation of room temperature superfluidity and novel nonlinear phenomena in plasmonic systems, challenging the common belief that absorption losses in metals prevent the realization of macroscopic quantum states.