Recent research in multi-principal element alloys (MPEAs) has increasingly focused on the role of short-range order (SRO) on material performance. However, the mechanisms of SRO formation and its precise control remain elusive, limiting the progress of SRO engineering. Here, leveraging advanced additive manufacturing techniques that produce samples with a wide range of cooling rates (up to 107 K s-1) and an enhanced semi-quantitative electron microscopy method, we characterize SRO in three CoCrNi-based face-centered-cubic (FCC) MPEAs. Surprisingly, irrespective of the processing and thermal treatment history, all samples exhibit similar levels of SRO. Atomistic simulations reveal that during solidification, prevalent local chemical order arises in the liquid-solid interface (solidification front) even under the extreme cooling rate of 1011 K s-1. This phenomenon stems from the swift atomic diffusion in the supercooled liquid, which matches or even surpasses the rate of solidification. Therefore, SRO is an inherent characteristic of most FCC MPEAs, insensitive to variations in cooling rates and even annealing treatments typically available in experiments.