After reprogramming to naïve pluripotency, human pluripotent stem cells (PSCs) still exhibit very low ability to make interspecies chimeras in mice and pigs. Whether this is because they are inherently devoid of the attributes of chimeric competency or because naïve PSCs in general cannot colonize embryos from distant species remains to be elucidated. Here, we have used different types of mouse, human and rhesus monkey naïve PSCs and we have analyzed their ability to colonize both distant (rabbit) and close (cynomolgus monkey) embryos. Mouse embryonic stem cells (ESCs) remained mitotically active after injection into rabbit and cynomolgus embryos and contributed to the formation of the neural tube in postimplantation rabbit embryos. In contrast, primate naive PSCs colonized rabbit and cynomolgus embryos with much lower efficiency, regardless of the reprogramming protocols. Unlike mouse ESCs, they slowed DNA replication following colony dissociation and, after injection into host embryos, they stalled in the G1 phase of the cell cycle and differentiated prematurely, regardless of host species, distant or close. These results show that, unlike mouse ESCs, primate naive PSCs do not make chimeras because they are inherently unfit to stay mitotically active during embryo colonization.