Line coincidence photopumping is a process where the electrons of an atomic or molecular species are radiatively excited through the absorption of line emission from another species at a coincident wavelength. There are many instances of line coincidence photopumping in astrophysical sources at optical and ultraviolet wavelengths, with the most famous example being Bowen fluorescence (pumping of O iii 303.80Å by He ii), but none to our knowledge in X-rays. However, here we report on a scheme where a He-like line of Ne ix at 11.000Å is photopumped by He-like Na x at 11.003Å, which predicts significant intensity enhancement in the Ne ix 82.76Å transition under physical conditions found in solar flare plasmas. A comparison of our theoretical models with published X-ray observations of a solar flare obtained during a rocket flight provides evidence for line enhancement, with the measured degree of enhancement being consistent with that expected from theory, a truly surprising result. Observations of this enhancement during flares on stars other than the Sun would provide a powerful new diagnostic tool for determining the sizes of flare loops in these distant, spatially-unresolved, astronomical sources.