It has been known for many years that an electron and its antiparticle, the positron, may together form a metastable hydrogen-like atom, known as positronium or Ps (ref. 1). In 1946, Wheeler speculated that two Ps atoms may combine to form the di-positronium molecule (Ps2), with a binding energy of 0.4eV. More recently, this molecule has been studied theoretically; however, because Ps has a short lifetime and it is difficult to obtain low-energy positrons in large numbers, Ps2 has not previously been observed unambiguously. Here we show that when intense positron bursts are implanted into a thin film of porous silica, Ps2 is created on the internal pore surfaces. We found that molecule formation occurs much more efficiently than the competing process of spin exchange quenching, which appears to be suppressed in the confined pore geometry. This result experimentally confirms the existence of the Ps2 molecule and paves the way for further multi-positronium work. Using similar techniques, but with a more intense positron source, we expect to increase the Ps density to the point where many thousands of atoms interact and can undergo a phase transition to form a Bose-Einstein condensate. As a purely leptonic, macroscopic quantum matter-antimatter system this would be of interest in its own right, but it would also represent a milestone on the path to produce an annihilation gamma-ray laser.