Highly charged iron (Fe(16+), here referred to as Fe XVII) produces some of the brightest X-ray emission lines from hot astrophysical objects, including galaxy clusters and stellar coronae, and it dominates the emission of the Sun at wavelengths near 15 ångströms. The Fe XVII spectrum is, however, poorly fitted by even the best astrophysical models. A particular problem has been that the intensity of the strongest Fe XVII line is generally weaker than predicted. This has affected the interpretation of observations by the Chandra and XMM-Newton orbiting X-ray missions, fuelling a continuing controversy over whether this discrepancy is caused by incomplete modelling of the plasma environment in these objects or by shortcomings in the treatment of the underlying atomic physics. Here we report the results of an experiment in which a target of iron ions was induced to fluoresce by subjecting it to femtosecond X-ray pulses from a free-electron laser; our aim was to isolate a key aspect of the quantum mechanical description of the line emission. Surprisingly, we find a relative oscillator strength that is unexpectedly low, differing by 3.6σ from the best quantum mechanical calculations. Our measurements suggest that the poor agreement is rooted in the quality of the underlying atomic wavefunctions rather than in insufficient modelling of collisional processes.