Pluripotent stem cells (PSCs) possess the following two main properties: self-renewal and pluripotency. Self-renewal is defined as the ability to proliferate in an undifferentiated state and pluripotency as the capacity to differentiate into cells of the three germ layers, i.e., ectoderm, mesoderm, and endoderm. PSCs are derived from early embryos as embryonic stem cells (ESCs) or are produced by reprogramming somatic cells into induced pluripotent stem cells (iPSCs). In mice, PSCs can be stabilized into two states of pluripotency, namely naive and primed. Naive and primed PSCs notably differ by their ability to colonize a host blastocyst to produce germline-competent chimeras; hence, naive PSCs are valuable for transgenesis, whereas primed PSCs are not. Thanks to its physiological and developmental peculiarities similar to those of primates, the rabbit is an interesting animal model for studying human diseases and early embryonic development. Both ESCs and iPSCs have been described in rabbits. They self-renew in the primed state of pluripotency and, therefore, cannot be used for transgenesis. This review presents the available data on the pluripotent state and the chimeric ability of these rabbit PSCs. It also examines the potential barriers that compromise their intended use as producers of germline-competent chimeras and proposes possible alternatives to exploit them for transgenesis.