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By measuring the transmission of near-resonant light through an atomic vapor confined in a nanocell we demonstrate a mesoscopic optical response arising from the nonlocality induced by the motion of atoms with a phase coherence length larger than the cell thickness. Whereas conventional dispersion theory-where the local atomic response is simply convolved by the Maxwell-Boltzmann velocity distribution-is unable to reproduce the measured spectra, a model including a nonlocal, size-dependent susceptibility is found to be in excellent agreement with the measurements. This result improves our understanding of light-matter interaction in the mesoscopic regime and has implications for applications where mesoscopic effects may degrade or enhance the performance of miniaturized atomic sensors.