Natural products provide a vast array of chemical structures to explore in the discovery of new medicines. Although secondary metabolites produced by microbes have been developed to treat a variety of diseases, including bacterial and fungal infections, to date there has been limited investigation of natural products with antiviral activity. In this report, we used a phenotypic cell-based replicon assay coupled with an iterative biochemical fractionation process to identify, purify, and characterize antiviral compounds produced by marine microbes. We isolated a compound from Streptomyces kaviengensis, a novel actinomycetes isolated from marine sediments obtained off the coast of New Ireland, Papua New Guinea, which we identified as antimycin A1a. This compound displays potent activity against western equine encephalitis virus in cultured cells with half-maximal inhibitory concentrations of less than 4 nM and a selectivity index of greater than 550. Our efforts also revealed that several antimycin A analogues display antiviral activity, and mechanism of action studies confirmed that these Streptomyces-derived secondary metabolites function by inhibiting the cellular mitochondrial electron transport chain, thereby suppressing de novo pyrimidine synthesis. Furthermore, we found that antimycin A functions as a broad spectrum agent with activity against a wide range of RNA viruses in cultured cells, including members of the Togaviridae, Flaviviridae, Bunyaviridae, Picornaviridae, and Paramyxoviridae families. Finally, we demonstrate that antimycin A reduces central nervous system viral titers, improves clinical disease severity, and enhances survival in mice given a lethal challenge with western equine encephalitis virus. Our results provide conclusive validation for using natural product resources derived from marine microbes as source material for antiviral drug discovery, and they indicate that host mitochondrial electron transport is a viable target for the continued development of broadly active antiviral compounds.