We propose a realization of Kondo-lattice physics in moiré superlattices at the interface between a WX2 homobilayer and MoX2 monolayer (where X=S,Se). Under appropriate gating conditions, the interface-WX2-layer forms a triangular lattice of local moments that couple to itinerant electrons in the other WX2-layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach we identify a range of twist-angles which support a gate-tuned quantum phase transition between a heavy-fermion liquid with large anomalous Hall conductance and a fractionalized chiral spin-liquid coexisting with a light Fermi liquid, and describe experimental signatures to distinguish among competing theoretical scenarios.