An exciton is an electron-hole bound pair in a semiconductor. In the low-density limit, it is a composite Bose quasi-particle, akin to the hydrogen atom. Just as in dilute atomic gases, reducing the temperature or increasing the exciton density increases the occupation numbers of the low-energy states leading to quantum degeneracy and eventually to Bose-Einstein condensation (BEC). Because the exciton mass is small--even smaller than the free electron mass--exciton BEC should occur at temperatures of about 1 K, many orders of magnitude higher than for atoms. However, it is in practice difficult to reach BEC conditions, as the temperature of excitons can considerably exceed that of the semiconductor lattice. The search for exciton BEC has concentrated on long-lived excitons: the exciton lifetime against electron-hole recombination therefore should exceed the characteristic timescale for the cooling of initially hot photo-generated excitons. Until now, all experiments on atom condensation were performed on atomic gases confined in the potential traps. Inspired by these experiments, and using specially designed semiconductor nanostructures, we have collected quasi-two-dimensional excitons in an in-plane potential trap. Our photoluminescence measurements show that the quasi-two-dimensional excitons indeed condense at the bottom of the traps, giving rise to a statistically degenerate Bose gas.