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The search for such a state was motivated by the recent discovery by the BaBar Collaboration of a narrow state at 2.32 GeV, the DsJ*(2317)+ that decays to Ds+pi0. Reconstructing the Ds+pi0 and Ds*+pi0 final states in CLEO data, we observe peaks in both of the corresponding reconstructed mass difference distributions, dM(Dspi0)=M(Dspi0)-M(Ds) and dM(Ds*pi0)=M(Ds*pi0)-M(Ds*), both of them at values near 350 MeV. 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