Interacting many-body systems are characterized by stable configurations of objects-ranging from elementary particles to cosmological formations(1-3)-that also act as building blocks for more complicated structures. It is often possible to incorporate interactions in theoretical treatments of crystalline solids by introducing suitable quasiparticles that have an effective mass, spin or charge(4,5) which in turn affects the material's conductivity, optical response or phase transitions(2,6,7). Additional quasiparticle interactions may also create strongly correlated configurations yielding new macroscopic phenomena, such as the emergence of a Mott insulator(8), superconductivity or the pseudogap phase of high-temperature superconductors(9-11). In semiconductors, a conduction-band electron attracts a valence-band hole (electronic vacancy) to create a bound pair, known as an exciton(12,13), which is yet another quasiparticle. Two excitons may also bind together to give molecules, often referred to as biexcitons(14), and even polyexcitons may exist(15,16). In indirect-gap semiconductors such as germanium or silicon, a thermodynamic phase transition may produce electron-hole droplets whose diameter can approach the micrometre range(17,18). In direct-gap semiconductors such as gallium arsenide, the exciton lifetime is too short for such a thermodynamic process. Instead, different quasiparticle configurations are stabilized dominantly by many-body interactions, not by thermalization. The resulting non-equilibrium quantum kinetics is so complicated that stable aggregates containing three or more Coulomb-correlated electron-hole pairs remain mostly unexplored. Here we study such complex aggregates and identify a new stable configuration of charged particles that we call a quantum droplet. This configuration exists in a plasma and exhibits quantization owing to its small size. It is charge neutral and contains a small number of particles with a pair-correlation function that is characteristic of a liquid. We present experimental and theoretical evidence for the existence of quantum droplets in an electron-hole plasma created in a gallium arsenide quantum well by ultrashort optical pulses.