An ideal one-dimensional (1D) magnet is expected to show exotic quantum phenomena. For compounds with larger S (S = 3/2, 2, 5/2, ...), however, a small interchain interaction J' tends to drive a conventional long-range ordered (LRO) state. Here, a new layered structure of FeF3(4,4'-bpy) (4,4'-bpy = 4,4'-bipyridyl) with novel S = 5/2 (Fe(3+)) chains has been hydrothermally synthesized by using 4,4'-bpy to separate chains. The temperature-dependent susceptibility exhibits a broad maximum at high as 164 K, suggesting a fairly strong Fe-F-Fe intrachain interaction J. However, no anomaly associated with a LRO is seen in both magnetic susceptibility and specific heat even down to 2 K. This indicates an extremely small J' with J'/J < 3.2 × 10(-5), making this new material a nearly ideal 1D antiferromagnet. Mössbauer spectroscopy at 2.7 K reveals a critical slowing down of the 1D fluctuations toward a possible LRO at lower temperatures.