We have previously argued that targeted interstellar communication has a physical optimum at narrowband X-ray wavelengths λ≈1nm, limited by the surface roughness of focusing devices at the atomic level (arXiv:1711.05761). We search 24,247 archival X-ray spectra (of 6,454 unique objects) for such features and present 19 sources with monochromatic signals. Close examination reveals that these are most likely of natural origin. The ratio of artificial to natural sources must be <0.01%. This first limit can be improved in future X-ray surveys.