Electron-positron pair plasmas represent a unique state of matter, whereby there exists an intrinsic and complete symmetry between negatively charged (matter) and positively charged (antimatter) particles. These plasmas play a fundamental role in the dynamics of ultra-massive astrophysical objects and are believed to be associated with the emission of ultra-bright gamma-ray bursts. Despite extensive theoretical modelling, our knowledge of this state of matter is still speculative, owing to the extreme difficulty in recreating neutral matter-antimatter plasmas in the laboratory. Here we show that, by using a compact laser-driven setup, ion-free electron-positron plasmas with unique characteristics can be produced. Their charge neutrality (same amount of matter and antimatter), high-density and small divergence finally open up the possibility of studying electron-positron plasmas in controlled laboratory experiments.