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CrAl₃Bi₂O₉ forms in a mullite-type structure characterized by linear chains of edge-sharing, Cr- and Al-centered octahedra. Measurements of dc magnetic susceptibility χ carried out on high quality single crystals of this compound reveal a fluctuating moment of 2.60 μ_B/Cr -- reduced from the 3.87 μ_B/Cr expected for Cr³⁺ -- while χ deviates from the Curie-Weiss law below temperature T ~ 50 K, remaining enhanced down at least to T = 3 K. The Weiss temperature Θ_W = -23 K suggests that the prevailing local moment interactions are antiferromagnetic in nature. Measurements of magnetization vs. field H below T = 10 K reveal deviations from H/T scaling, suggesting that the additional contribution to χ is not Brillouin-like. UV/Vis spectroscopy reveals a rapid increase in absorption corresponding to transitions across an insulating gap of ~ 3 eV, slightly larger than the DFT direct gap of Al₄Bi₂O₉.