Diversification of antiretroviral factors during host evolution has erected formidable barriers to cross-species retrovirus transmission. This phenomenon likely protects humans from infection by many modern retroviruses, but it has also impaired the development of primate models of HIV-1 infection. Indeed, rhesus macaques are resistant to HIV-1, in part due to restriction imposed by the TRIM5α protein (rhTRIM5α). Initially, we attempted to derive rhTRIM5α-resistant HIV-1 strains using two strategies. First, HIV-1 was passaged in engineered human cells expressing rhTRIM5α. Second, a library of randomly mutagenized capsid protein (CA) sequences was screened for mutations that reduced rhTRIM5α sensitivity. Both approaches identified several individual mutations in CA that reduced rhTRIM5α sensitivity. However, neither approach yielded mutants that were fully resistant, perhaps because the locations of the mutations suggested that TRIM5α recognizes multiple determinants on the capsid surface. Moreover, even though additive effects of various CA mutations on HIV-1 resistance to rhTRIM5α were observed, combinations that gave full resistance were highly detrimental to fitness. Therefore, we employed an ‘assisted evolution’ approach in which individual CA mutations that reduced rhTRIM5α sensitivity without fitness penalties were randomly assorted in a library of viral clones containing synthetic CA sequences. Subsequent passage of the viral library in rhTRIM5α-expressing cells resulted in the selection of individual viral species that were fully fit and resistant to rhTRIM5α. These viruses encoded combinations of five mutations in CA that conferred complete or near complete resistance to the disruptive effects of rhTRIM5α on incoming viral cores, by abolishing recognition of the viral capsid. Importantly, HIV-1 variants encoding these CA substitutions and SIV_mac239 Vif replicated efficiently in primary rhesus macaque lymphocytes. These findings demonstrate that rhTRIM5α is difficult to but not impossible to evade, and doing so should facilitate the development of primate models of HIV-1 infection.