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Using 13.5 fb-1 of e+e- annihilation data collected with the CLEO II detector, we have observed a narrow resonance decaying to Ds*+π0 with a mass near 2.46 GeV/c2. The search for such a state was motivated by the recent discovery by the BaBar Collaboration of a narrow state at 2.32 GeV/c2, the DsJ*(2317) +, that decays to Ds+ π0. Reconstructing the Ds+ π0 and Ds*+ π0 final states in CLEO data, we observe peaks in both of the corresponding reconstructed mass difference distributions, ΔM(Ds π0) = M (Ds π0)–M (Ds) and ΔM(Ds* π0) = M (Ds* π0)–M (Ds*), both of them at values near 350 MeV/c2. We interpret these peaks as signatures of two distinct states, the DsJ* (2317)+ plus a new state, designated as the DsJ(2463) +. Because of the similar ΔM values, each of these states represents a source of background for the other if photons are lost, ignored or added. A quantitative accounting of these reflections confirms that both states exist. We have measured the mean mass differences < ΔM (Dsπ0)> = 350.0±1.2 (stat)±1.0 (syst) MeV/c2 for the DsJ* (2317)+ state, and < ΔMDs* π0)> = 351.2±1.7 (stat)±1.0 (syst) MeV/c2 for the new DsJ(2463)+ state. We have also searched, but find no evidence, for decays of the two states via the channels Ds*+ γ, Ds+ γ, and Ds+ π sup>+ π sup>-. The observations of the two states at 2.32 and 2.46 GeV/c2, in the Ds+ π0 and Ds*+ π0 decay channels, respectively, are consistent with their interpretations as cs-bar mesons with an orbital angular momentum L = 1 and spin and parity JP = 0+ and 1+.