Recognizing fossil microorganisms is essential to the study of life's origin and evolution and to the ongoing search for life on Mars. Purported fossil microbes in ancient rocks include common assemblages of iron-mineral filaments and tubes. Recently, such assemblages have been interpreted to represent Earth's oldest body fossils, Earth's oldest fossil fungi, and Earth's best analogues for fossils that might form in the basaltic Martian subsurface. Many of these putative fossils exhibit hollow circular cross-sections, lifelike (non-crystallographic, constant-thickness, and bifurcate) branching, anastomosis, nestedness within ‘sheaths’, and other features interpreted as strong evidence for a biological origin, since no abiotic process consistent with the composition of the filaments has been shown to produce these specific lifelike features either in nature or in the laboratory. Here, I show experimentally that abiotic chemical gardening can mimic such purported fossils in both morphology and composition. In particular, chemical gardens meet morphological criteria previously proposed to establish biogenicity, while also producing the precursors to the iron minerals most commonly constitutive of filaments in the rock record. Chemical gardening is likely to occur in nature. Such microstructures should therefore not be assumed to represent fossil microbes without independent corroborating evidence.