The crystallization of complex, concentrated alloys can result in atomic-level short-range order, composition gradients, and phase separation. These features govern the properties of the resulting alloy. While nucleation and growth in single-element metals are well understood, several open questions remain regarding the crystallization of multi-principal component alloys. We use molecular dynamics to model the crystallization of a five-element, equiatomic alloy modeled after CoCrCuFeNi upon cooling from the melt. Stochastic, homogeneous nucleation results in nuclei with a biased composition distribution, rich in Fe and Co. This deviation from the random sampling of the overall composition is driven by the internal energy and affects nuclei of a wide range of sizes, from tens of atoms all the way to super-critical sizes. This results in short-range order and compositional gradients at nanometer scales.