Brillouin scattering measurements of the single-crystal elastic properties of the as-made zeolite silicalite mid R:(C(3)H(7))(4)NFmid R:(4)[Si(96)O(192)]-MFI provides the first experimental evidence for on-axis negative Poisson's ratios (auxeticity) in a synthetic zeolite structure. MFI laterally contracts when compressed and laterally expands when stretched along x(1) and x(2) directions in the (001) plane (nu(12)=-0.061, nu(21)=-0.051). The aggregate Poisson's ratio of MFI, although positive, has an anomalously low value nu=0.175(3) compared to other silicate materials. These results suggest that the template-free MFI-silicalite [Si(96)O(192)] might have potential applications as tunable sieve where molecular discriminating characteristics are adjusted by application of stress along specific axes.