We report the first experimental observation of self-trapped Airy beams in a nonlinear medium. As opposed to screening or photovoltaic spatial solitons, this new class of self-localized beams owes its existence to carrier diffusion effects. The asymmetric action of two-wave mixing supports the asymmetric intensity profile of the Airy states, with a balance that is independent of the beam intensity (unlike solitons). Further, the self-trapped wave packets self-bend during propagation at an acceleration rate that is independent of the thermal energy associated with the diffusive nonlinearity.