No effective therapeutic is currently in place for improved case management of severe measles or the rapid control of outbreaks. Through high-throughput screening, we recently identified a novel small-molecule class that potently blocks activity of the measles virus (MeV) RNA-dependent RNA polymerase (RdRp) complex in transient replicon assays. However, the nature of the block in RdRp activity and the physical target of the compound remained elusive. Through real-time reverse transcription-PCR analysis, we demonstrate that the lead compound AS-136A blocks viral RNA synthesis in the context of an infection. Adaptation of different MeV strains to growth in the presence of the compound identified three candidate hot spots for resistance that are located in conserved domains of the viral polymerase (L protein) subunit of the RdRp complex. Rebuilding of individual mutations in RdRp-driven reporter assays and recombinant MeV traced the molecular basis for resistance to specific mutations in L. Mutations responsible for resistance cluster in the immediate vicinity of the proposed catalytic center for phosphodiester bond formation and neighboring conserved domains of L, providing support for effective inhibition of a paramyxovirus RdRp complex through interaction of a nonnucleoside small-molecule inhibitor with the L protein. Resistance mutations are located in regions of L that are fully conserved among viral isolates, and recombinant MeV harboring individual resistance mutations show some delay in the onset of viral growth in vitro. Taken together, these data support the hypothesis that acquiring mutations in these L domains may reduce virus fitness.