We produce the first experimental evidence of x-ray natural circular dichroism (XNCD) in a uniaxial gyrotropic crystal of alpha-LiIO3 that is known to crystallize with space group P6(3) and to exhibit a very strong nonlinear susceptibility. For the sake of simplicity, the optical axis was set colinear to the direction of the exciting x-ray beam in order to get rid of undesirable birefringence and linear dichroism effects. The nicely structured XNCD spectra recorded at the L-I, L-II, and L-III edges of iodine are assigned to the electric dipole-electric quadrupole (E1.E2) interference terms which do not vanish in gyrotropic crystals but contribute to a second order polarizability. Our interpretation is consistent with a band structure calculation and is fully supported by ab initio multiple scattering simulations. The signatures recorded at the L-II and L-III edges are similar and have the same sign. This is in contrast to x-ray magnetic circular dichroism (XNCD) spectra which usually exhibit opposite signs at the L-II and L-III edges : while the exchange and spin-orbit interactions are the driving terms in XMCD, this is not the case in XNCD. The XNCD signal detected at the L-I edge is found to be relatively more intense and has the opposite sign. These results leave very little space for a contribution of the electric dipole-magnetic dipole (E1.M1) interference terms which are usually dominant at optical wavelengths but should be barely detectable in the x-ray range.