Based on three years of deep observations of the Galactic center with the Chandra X-ray Observatory, we report the discovery of changes in the intensities and morphologies of two hard X-ray nebulosities. The nebulosities are dominated by fluorescent iron emission, and are coincident with molecular clouds. The morphological changes are manifest on parsec scales, which requires that these iron features are scattered X-rays from a 2 or 3-year-long outburst of a point source (either \sgrastar or an X-ray binary) with a luminosity of at least 1037 erg s-1. The variability precludes the hypotheses that these nebulae either are produced by keV electrons bombarding molecular clouds, or are iron-rich ejecta from supernovae. Moreover, the morphologies of the reflection nebulae implies that the dense regions of the clouds are filamentary, with widths of 0.3 pc and lengths of 2 pc.