Li metal is among the most attractive anode materials for secondary batteries, with a theoretical specific capacity > 3800 mAh g-1. However, its extremely low electrochemical potential is associated with high chemical reactivity that results in undesirable reduction of electrolyte species on the lithium surface, leading to spontaneous formation of a solid electrolyte interphase (SEI) with uncontrolled composition, morphology, and physicochemical properties. Here, we demonstrate a new approach to stabilize Li metal anodes using a hybrid organic/inorganic artificial solid electrolyte interphase (ASEI) deposited directly on the Li metal surface by self-healing electrochemical polymerization (EP) and atomic layer deposition (ALD). This hybrid protection layer is thin, flexible, ionically conductive, and electrically insulating. We show that Li metal protected by the hybrid protection layer gives rise to very stable cycling performance for over 300 cycles at current density 1 mA/cm2 and over 110 cycles at current density 2 mA/cm2, well above the threshold for dendrite growth at unprotected Li. Our strategy for protecting Li metal anodes by hybrid organic/inorganic ASEI represents a new approach to mitigating or eliminating dendrite formation at reactive metal anodes - illustrated here for Li - and may expedite the realization of a "beyond-Li-ion" battery technology employing Li metal anodes (e.g., Li-S).