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A<sc>bstract</sc> We study the generation of the baryon asymmetry in Composite Higgs models with partial compositeness of the Standard Model (SM) fermions and heavy right-handed neutrinos, developing for the first time a complete picture of leptogenesis in that setup. The asymmetry is induced by the out of equilibrium decays of the heavy right-handed neutrinos into a plasma of the nearly conformal field theory (CFT), i.e. the deconfined phase of the Composite Higgs dynamics. This exotic mechanism, which we callConformal Leptogenesis, admits a reliable description in terms of a set of “Boltzmann equations” whose coefficients can be expressed in terms of correlation functions of the CFT. The asymmetry thus generated is subsequently affected by the supercooling resulting from the confining phase transition of the strong Higgs sector as well as by the washout induced by the resonances formed after the transition. Nevertheless, a qualitative description of the latter effects suggests that conformal leptogenesis can successfully reproduce the observed baryon asymmetry in a wide region of parameter space. A distinctive signature of our scenarios is a sizable compositeness forallthe generations of SM neutrinos, which is currently consistent with all constraints but may be within reach of future colliders.