LEUTX is a homeodomain transcription factor expressed in the very early embryo with a function around embryonic genome activation. The LEUTX gene is found only in eutherian mammals including humans but, unlike the majority of homeobox genes, the encoded amino acid sequence is very different between divergent mammalian species. However, whether dynamic evolution has also occurred between closely related mammalian species remains unclear. In this work, we perform a comparative genomics study of LEUTX within the primates, revealing dramatic evolutionary sequence change between closely related species. Positive selection has acted on sites in the LEUTX protein, including six sites within the homeodomain; this suggests that selection has driven changes in the set of downstream targets. Transfection into cell culture followed by transcriptomic analysis reveals small functional differences between human and marmoset LEUTX, suggesting rapid sequence evolution has fine-tuned the role of this homeodomain protein within the primates.