Entanglement occupies a peculiar position in quantum mechanics (QM). It occurs in quantum systems that consist of space-like separated parts or—more generally—in systems whose observables belong to disjoint Hilbert spaces. The latter is the case with single-neutron systems. Here, we report on a neutron polarimetric experiment, where a triply entangled Greenberger–Horne–Zeilinger state is exploited. The entanglement of spin, momentum and total energy degree of freedom is generated utilizing a suitable combination of radio-frequency and static magnetic fields. An average deviation of expectation values from theory—ideal circumstances—of 0.016(1) confirms the predictions of QM with high accuracy, demonstrating the high-efficiency manipulation of the entangled single-neutron system.