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We have observed resonant coherent excitation (RCE) of H-like Ar(17+) ions traveling through a 1 microm-thick Si crystal at an energy of 391 MeV/u in the nonchanneling condition. A three-dimensional periodic array of atomic planes induces RCE of the nonchanneling ions. The high energy heavy ions together with the thin crystal allow us to observe this new RCE through the measurements of the charge-state distribution of the emerging ions. The observed resonances are much narrower than those of planar-channeling ions due to the absence of the large Stark shift caused by the planar potential.