Recently, resonant two-photon ionization experiments on isolated adenine and adenosine suggested that adenosine exhibits a significantly shorter excited-state lifetime than adenine, which indicates the existence of an efficient excited-state deactivation mechanism in adenosine that is not existent in adenine. We report on ab initio investigations on a syn and an anti conformer of adenosine exhibiting an intramolecular O-H···N3 hydrogen bond. For both conformers, we have identified the existence of a barrierless excited-state deactivation mechanism that involves the forward-backward transfer of a proton along the intramolecular hydrogen bond and ultrafast radiationless deactivation through conical intersections. The S1/S0 conical intersection associated with the proton-transfer process is lower in energy than the known S1/S0 conical intersections associated with the excited-state deactivation processes inherent to the adenine moiety. These results support the conjecture that the photochemistry of hydrogen bonds plays a decisive role for the photostability of the molecular building blocks of RNA and DNA, which have been selected at the earliest stages of the chemical evolution of life.