Plasmonics in topological semimetals offers exciting opportunities for fundamental physics exploration as well as for technological applications. Here, we investigate plasmons in the exemplar chiral crystal CoSi, which hosts a variety of multifold fermionic excitations. We show that CoSi hosts two distinct plasmon modes in the infrared regime at 0.1 eV and 1.1 eV in the long-wavelength limit. The 0.1 eV plasmon is found to be highly dispersive, and originates from intraband collective oscillations associated with double spin-1 excitation, while the 1.1 eV plasmon is dispersionless and it involves interband correlations. Both plasmon modes lie outside the particle-hole continuum and possess a long lifetime. Our study indicates that the CoSi class of materials will provide an interesting materials platform for exploring fundamental and technological aspects of topological plasmonics.