Microcavity polaritons are composite half-light half-matter quasiparticles, which have recently been demonstrated to exhibit rich physical properties, such as non-equilibrium condensation, parametric scattering and superfluidity. At the same time, polaritons have important advantages over photons for information processing, because their excitonic component leads to weaker diffraction and stronger interparticle interactions, implying, respectively, tighter localization and lower powers for nonlinear functionality. Here, we present the first experimental observations of bright polariton solitons in a strongly coupled semiconductor microcavity. The polariton solitons are shown to be micrometre-scale localized non-diffracting wave packets with a corresponding broad spectrum in momentum space. Unlike the solitons known in Bose condensed atomic gases, they are non-equilibrium and rely on a balance between losses and external pumping. Microcavity polariton solitons are excited on picosecond timescales, and thus have further benefits for information processing over light-only solitons in semiconductor cavity lasers, which have nanosecond response times.