The fossil record suggests that chordates might have been minor components of marine ecosystems during the first major diversification of animal life in the Cambrian. Vertebrates are represented by a handful of rare soft-bodied stem-lineage taxa known from Konservat-Lagerstätten, including Myllokunmingia and Yunnanozoon from the Stage 3 of South China, and Emmonsaspis and Metaspriggina from Stage 4-Drumian deposits of northeast USA and British Columbia. Here, we describe the first soft-bodied vertebrate from the American Great Basin, a region home to a dozen Cambrian Konservat-Lagerstätten. Found in the Drumian Marjum Formation of Utah, Nuucichthys rhynchocephalus gen. et sp. nov. is characterized by a finless torpedo-shaped body that includes a snout-like anterior head bearing anterolateral eyes, approximately 25 thick myomeres, a large branchial chamber with a keel and approximately seven putative dorsal bars and a spiniform caudal process. Using Bayesian inference, our analysis recovers Nuucichthys within the vertebrate stem, closer to the crown than Pikaia, Yunnanozoon and Myllokunmingia, where it forms a polytomy with its Laurentian relatives, Emmonsaspis and Metaspriggina, and a scion consisting of conodonts and crown-group vertebrates. Based on the eye orientation and absence of fins, we tentatively reconstruct Nuucichthys as a pelagic organism with limited swimming abilities (planktonektic).