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The 3d transition metal insulator Bi2CrAl3O9 forms with a quasi-one-dimensional structure characterized by linear chains of edge-sharing, Cr-and Al-centered, distorted octahedra. The UV/Vis spectrum of high-quality single crystals is marked by broad absorption edges corresponding to direct transitions across a 1.36-eV insulating gap. Measurements of dc magnetic susceptibility χ reveal a fluctuating moment of 2.60±0.01μB/Cr—reduced from the 3.87μB/Cr expected for Cr3+, while the Weiss temperature ΘW=−21±1 K implies that the prevailing local moment interactions are weakly antiferromagnetic in nature. Some 10% of the fluctuating moment is quenched, presumably due to the onset of an antiferromagnetic or spin glass phase at temperature T★=98±3 K, while measurements of magnetization versus field H at T≤10 K scale as H/T0.68(4), suggesting the presence of quantum fluctuations associated with a disordered phase. Density functional theory calculations carried out within the generalized gradient approximation are in excellent agreement with experimental results, asserting that short-range magnetic interactions remnant above T★ stabilize the insulating state