We demonstrate with accurate scattering calculations that a system constituted by a single quantum emitter (a semiconductor quantum dot) placed in the gap between two metallic nanoparticles can display the vacuum Rabi splitting. The largest dimension of the investigated system is only 36 nm. This nonperturbative regime is highly desirable for many possible applications in quantum information processing or schemes for controlling individual photons. Along this road, it will be possible to implement scalable photonic quantum computation without renouncing to the nanometric size of the classical logic gates of the present most compact electronic technology.