We detect a weak unidentified emission line at E=(3.55-3.57)+/-0.03 keV in a stacked XMM spectrum of 73 galaxy clusters spanning a redshift range 0.01-0.35. MOS and PN observations independently show the presence of the line at consistent energies. When the full sample is divided into three subsamples (Perseus, Centaurus+Ophiuchus+Coma, and all others), the line is significantly detected in all three independent MOS spectra and the PN all others spectrum. It is also detected in the Chandra spectra of Perseus with the flux consistent with XMM (though it is not seen in Virgo). However, it is very weak and located within 50-110eV of several known faint lines, and so is subject to significant modeling uncertainties. On the origin of this line, we argue that there should be no atomic transitions in thermal plasma at this energy. An intriguing possibility is the decay of sterile neutrino, a long-sought dark matter particle candidate. Assuming that all dark matter is in sterile neutrinos with m_s=2E=7.1 keV, our detection in the full sample corresponds to a neutrino decay mixing angle sin^2(2theta)=7e-11, below the previous upper limits. However, based on the cluster masses and distances, the line in Perseus is much brighter than expected in this model. This appears to be because of an anomalously bright line at E=3.62 keV in Perseus, possibly an Ar XVII dielectronic recombination line, although its flux would be 30 times the expected value and physically difficult to understand. In principle, such an anomaly might explain our line detection in other subsamples as well, though it would stretch the line energy uncertainties. Another alternative is the above anomaly in the Ar line combined with the nearby 3.51 keV K line also exceeding expectation by factor 10-20. Confirmation with Chandra and Suzaku, and eventually Astro-H, are required to determine the nature of this new line.(ABRIDGED)
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