The first measurements of forward multijet rates in deep-inelastic lepton scattering are presented. Data were taken with a 490-GeV muon beam incident on a hydrogen target. The jets were defined using the gade algorithm. The measured rates are presented as a function of the jet resolution parameter ${\mathit{y}}_{\mathrm{cut}}$, and as a function of the virtual-photon--proton center-of-momentum energy W, in the range 13\ensuremath{\le}W\ensuremath{\le}33 GeV. Comparisons are made to the predictions of the Lund Monte Carlo programs and good agreement is obtained when QCD corrections are included in the model.