Using 13.5 fb-1 of e+e- annihilation data collected with the CLEO II detector, we have observed a narrow resonance decaying to D*s + 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/c 2, the D*sJ(2317)+, that decays to D s + π0. Reconstructing the Ds + π0 and D*s + π0 final states in CLEO data, we observe peaks in both of the corresponding reconstructed mass difference distributions, ΔM(D sπ0) = M(Dsπ0) - M(D s) and ΔM(D*s π0) = M(D*s π0) - M(D*s), both of them at values near 350 MeV/c2. We interpret these peaks as signatures of two distinct states, the D*sJ(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(Ds π0)〉 = 350.0 ±1.2 (stat) ± 1.0 (syst) MeV/c2 for the D*sJ(2317)+ state, and 〈ΔM(D* s 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 D*s + γ, Ds + γ, and Ds + π+ π-. The observations of the two states at 2.32 and 2.46 GeV/c2, in the D s + π0 and D*s + π0 decay channels, respectively, are consistent with their interpretations as cs̄ mesons with an orbital angular momentum L = 1 and spin and parity JP = 0+ and 1+.