A narrow state, which we label D-sJ(2458)(+), with a mass 2458.0+/-1.0 (stat)+/-1.0 (syst) MeV/c(2), is observed in the inclusive D(s)(+)pi(0)gamma mass distribution in 91 fb(-1) of e(+)e(-) annihilation data recorded by the BABAR detector at the SLAC PEP-II asymmetric-energy e(+)e(-) storage ring. The observed width is consistent with the experimental resolution. The data favor decay through D-s(*)(2112)(+)pi(0) rather than through D-sJ(*)(2317)(+)gamma. An analysis of D(s)(+)pi(0) data accounting for the influence of the D-sJ(2458)(+) produces a D-sJ(*)(2317)(+) mass of 2317.3+/-0.4 (stat)+/-0.8 (syst) MeV/c(2).