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*+sπ0 with a mass near 2.46GeV/c2. The search for such a state was motivated by the recent discovery by the BaBar Collaboration of a narrow state at 2.32GeV/c2, the D*sJ(2317)+, that decays to D+sπ0. Reconstructing the D+sπ0 and D*+sπ0 final states in CLEO data, we observe peaks in both of the corresponding reconstructed mass difference distributions, ΔM(Dsπ0)=M(Dsπ0)−M(Ds) and ΔM(D*sπ0)=M(D*sπ0)−M(D*s), both of them at values near 350MeV/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(Dsπ0)⟩=350.0±1.2(stat)±1.0(syst)MeV/c2 for the D*sJ(2317)+ state, and ⟨ΔM(D*sπ0)⟩=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*+sγ,D+sγ, and D+sπ+π−. The observations of the two states at 2.32 and 2.46GeV/c2, in the D+sπ0 and D*+sπ0 decay channels, respectively, are consistent with their interpretations as c¯s mesons with an orbital angular momentum L=1 and spin and parity JP=0+ and 1+. Received 28 May 2003Corrected 6 June 2007DOI:https://doi.org/10.1103/PhysRevD.68.032002©2003 American Physical Society