Recently, new reactor antineutrino spectra have been provided for 235 U, 239 Pu, 241 Pu, and 238 U, increasing the mean flux by about 3 percent. To a good approximation, this reevaluation applies to all reactor neutrino experiments. The synthesis of published experiments at reactor-detector distances < 100 m leads to a ratio of observed event rate to predicted rate of 0.976±0.024. With our new flux evaluation, this ratio shifts to 0.943±0.023, leading to a deviation from unity at 98.6% C.L. which we call the reactor antineutrino anomaly. The compatibility of our results with the existence of a fourth non-standard neutrino state driving neutrino oscillations at short distances is discussed. The combined analysis of reactor data, gallium solar neutrino calibration experiments, and MiniBooNEν data disfavors the no-oscillation hypothesis at 99.8% C.L. The oscillation parameters are such that |∆m 2 new | > 1.5 eV 2 (95%) and sin 2 (2θnew) = 0.14 ± 0.08 (95%). Constraints on the θ13 neutrino mixing angle are revised.