The majority of recently emerging infectious diseases in humans is due to cross-species pathogen transmissions from animals. To establish a productive infection in new host species, viruses must overcome barriers to replication mediated by diverse and rapidly evolving host restriction factors such as protein kinase R (PKR). Many viral antagonists of these restriction factors are species specific. For example, the rhesus cytomegalovirus PKR antagonist, RhTRS1, inhibits PKR in some African green monkey (AGM) cells, but does not inhibit human or rhesus macaque PKR. To model the evolutionary changes necessary for cross-species transmission, we generated a recombinant vaccinia virus that expresses RhTRS1 in a strain that lacks PKR inhibitors E3L and K3L (VVΔEΔK+RhTRS1). Serially passaging VVΔEΔK+RhTRS1 in minimally-permissive AGM cells increased viral replication 10- to 100-fold. Notably, adaptation in these AGM cells also improved virus replication 1000- to 10,000-fold in human and rhesus cells. Genetic analyses including deep sequencing revealed amplification of the rhtrs1 locus in the adapted viruses. Supplying additional rhtrs1 in trans confirmed that amplification alone was sufficient to improve VVΔEΔK+RhTRS1 replication. Viruses with amplified rhtrs1 completely blocked AGM PKR, but only partially blocked human PKR, consistent with the replication properties of these viruses in AGM and human cells. Finally, in contrast to AGM-adapted viruses, which could be serially propagated in human cells, VVΔEΔK+RhTRS1 yielded no progeny virus after only three passages in human cells. Thus, rhtrs1 amplification in a minimally permissive intermediate host was a necessary step, enabling expansion of the virus range to previously nonpermissive hosts. These data support the hypothesis that amplification of a weak viral antagonist may be a general evolutionary mechanism to permit replication in otherwise resistant host species, providing a molecular foothold that could enable further adaptations necessary for efficient replication in the new host.