Flavor deconstruction refers to non-universal gauge extensions where the original gauge symmetry is deconstructed into separate copies, one for each family. A hierarchical chain of symmetry breaking provides an attractive low-scale solution to the flavor puzzle, consistent with flavor-changing neutral currents and finite naturalness. Although successful in explaining the origin of flavor hierarchies in the quark and charged lepton sectors, existing models have struggled with the large and seemingly anarchic mixing observed in neutrino oscillations. This letter identifies conditions under which neutrino anarchy may arise from flavor deconstruction in generic models with right-handed neutrinos. When deconstruction is applied to carefully chosen subgroups of the extended gauge symmetry, hierarchies in the seesaw formula cancel out.