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One of the main difficulties of observing many-body localization in natural solid-state materials is creating strong enough disorder. A strong random local magnetic field is difficult to achieve in a solid state material. We propose exploiting large random magnetic anisotropy, either in magnitude or direction, which can be realized in organometallic quantum magnets. We present the phase diagram of an S=1 Heisenberg chain in terms of both a random magnetic anisotropy and a random magnetic field. The many-body localization phase emerges with sufficiently large anisotropy under very small random fields. We propose candidate materials of doped single-chain organometallic quantum magnets for realizing many-body localization, where either orientation disorder or substitution of metal ions can create large random magnetic anisotropy required in our prediction.