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We demonstrate the feasibility of near edge x-ray absorption fine structure spectroscopy on solids by means of femtosecond soft x-ray pulses from a free-electron laser (FEL). Our experiments, carried out at the FEL at Hamburg used a special sample geometry, spectrographic energy dispersion, single shot position-sensitive detection, and a data normalization procedure that eliminates the severe fluctuations of the incident intensity in space and photon energy. As an example, we recorded the
D
3
1
N
4
,
5
edge absorption resonance of
La
3
+
ions in
LaMnO
3
. Our study opens the door for x-ray absorption measurements on future x-ray FEL facilities.