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I will present a novel method for probing extremely weak large-scale magnetic fields in the intergalactic medium prior to the epoch of reionization. This method relies on the effect of spin alignment of hydrogen atoms in a cosmological setting, and on the effect of magnetic precession of the atoms on the statistics of the 21–cm brightness–temperature fluctuations. It is intrinsically sensitive to magnetic fields weaker than 10^{-19} Gauss in physical units, and thus has a potential to reach many orders of magnitude below the current constraints on primordial magnetic fields. I will discuss the physical mechanism, lay out the estimator formalism that enables searches with future 21-cm tomographic surveys, and present forecasts for detecting magnetic fields in the high-redshift universe using this method.