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 303.80 Å 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 11.000 Å is photopumped by He-like Na X at 11.003 Å, which predicts significant intensity enhancement in the Ne IX 82.76 Å 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.