Resonant and off-resonant Raman Optical Activity signals in the X-ray regime (XROA) are predicted. XROA is a chiral-sensitive variant of the spontaneous Resonant Inelastic Scattering (RIXS) signal. Thanks to the highly localized nature of core excitations, these signals provide a direct probe of local chirality with high sensitivity to the molecular structure. We derive sum-over-states expressions for frequency domain XROA signals and apply them to tyrosine at the nitrogen and oxygen K-edges. Time-resolved extensions of ROA made possible by using additional pulses are briefly outlined.