A crucial step in the arenavirus life cycle is the biosynthesis of the viral envelope glycoprotein (GP) responsible for virus attachment and entry. Processing of the GP precursor (GPC) by the cellular proprotein convertase site 1 protease (S1P), also known as subtilisin-kexin-isozyme 1 (SKI-1), is crucial for cell-to-cell propagation of infection and production of infectious virus. Here, we sought to evaluate arenavirus GPC processing by S1P as a target for antiviral therapy using a recently developed peptide-based S1P inhibitor, decanoyl (dec)-RRLL-chloromethylketone (CMK), and the prototypic arenavirus lymphocytic choriomeningitis virus (LCMV). To control for off-target effects of dec-RRLL-CMK, we employed arenavirus reverse genetics to introduce a furin recognition site into the GPC of LCMV. The rescued mutant virus grew to normal titers, and the processing of its GPC critically depended on cellular furin, but not S1P. Treatment with the S1P inhibitor dec-RRLL-CMK resulted in specific blocking of viral spread and virus production of LCMV. Combination of the protease inhibitor with ribavirin, currently used clinically for treatment of human arenavirus infections, resulted in additive drug effects. In cells deficient in S1P, the furin-dependent LCMV variant established persistent infection, whereas wild-type LCMV underwent extinction without the emergence of S1P-independent escape variants. Together, the potent antiviral activity of an inhibitor of S1P-dependent GPC cleavage, the additive antiviral effect with ribavirin, and the low probability of emergence of S1P-independent viral escape variants make S1P-mediated GPC processing by peptide-derived inhibitors a promising strategy for the development of novel antiarenaviral drugs.