The nervous system provides a fundamental source of data for understanding the evolutionary relationships between major arthropod groups. Fossil arthropods rarely preserve neural tissue. As a result, inferring sensory and motor attributes of Cambrian taxa has been limited to interpreting external features, such as compound eyes or sensilla decorating appendages, and early-diverging arthropods have scarcely been analysed in the context of nervous system evolution. Here we report exceptional preservation of the brain and optic lobes of a stem-group arthropod from 520 million years ago (Myr ago), Fuxianhuia protensa, exhibiting the most compelling neuroanatomy known from the Cambrian. The protocerebrum of Fuxianhuia is supplied by optic lobes evidencing traces of three nested optic centres serving forward-viewing eyes. Nerves from uniramous antennae define the deutocerebrum, and a stout pair of more caudal nerves indicates a contiguous tritocerebral component. Fuxianhuia shares a tripartite pre-stomodeal brain and nested optic neuropils with extant Malacostraca and Insecta, demonstrating that these characters were present in some of the earliest derived arthropods. The brain of Fuxianhuia impacts molecular analyses that advocate either a branchiopod-like ancestor of Hexapoda or remipedes and possibly cephalocarids as sister groups of Hexapoda. Resolving arguments about whether the simple brain of a branchiopod approximates an ancestral insect brain or whether it is the result of secondary simplification has until now been hindered by lack of fossil evidence. The complex brain of Fuxianhuia accords with cladistic analyses on the basis of neural characters, suggesting that Branchiopoda derive from a malacostracan-like ancestor but underwent evolutionary reduction and character reversal of brain centres that are common to hexapods and malacostracans. The early origin of sophisticated brains provides a probable driver for versatile visual behaviours, a view that accords with compound eyes from the early Cambrian that were, in size and resolution, equal to those of modern insects and malacostracans.