Near-equiatomic multi-component high-entropy alloys (HEAs) have engendered much attention of late due to the remarkable mechanical properties of some of these new metallic materials. In particular, one of the first reported HEAs, the equiatomic, single-phase, face-centered cubic (fcc) alloy CrMnFeCoNi, often termed the Cantor alloy, has been shown to display an exceptional combination of strength, ductility and fracture toughness, i.e., damage tolerance, at room temperature, properties that are further enhanced at cryogenic temperatures. Despite this alloy being the most studied HEA to date, its resistance to crack growth under cyclic fatigue loading has not yet been characterized. Here, we examine its fatigue-crack propagation behavior, primarily at lower, near-threshold, growth rates, both at room temperature (293 K) and at 198 K. At 293 K, the alloy shows a fatigue threshold, ΔKTH, of ∼4.8 MPa√m, which increases by more than 30% to ΔKTH ∼6.3 MPa√m with decrease in temperature to 198 K; additionally, the Paris exponent m was found to increase from roughly 3.5 to 4.5 with decreasing temperature. Examination of the fracture surfaces and crack paths indicate a transition from predominantly transgranular crack propagation at room temperature to intergranular-dominated failure at the lower temperature. Such a change in crack path is generally associated with an increasing degree of physical contact between the two fracture surfaces, i.e., roughness-induced fatigue crack closure, which is likely to be the main reason for the difference in the measured thresholds. Additionally, we believe that the higher thresholds found at 198 K are associated with the alloy's higher strength at lower temperatures, which both reduces the crack-tip opening displacements at a given stress-intensity range and prevents plastic deformations of the grains in the wake of the crack. At room temperature, such plastically deformed grains can be associated with a loss of contact shielding of the crack-tip through closure, resulting in a lower threshold compared to 198 K.