  The Kochen-Specker theorem theoretically shows evidence of the
incompatibility of noncontextual hidden variable theories with quantum
mechanics. Quantum contextuality is a more general concept than quantum
non-locality which is quite well tested in experiments by using Bell
inequalities. Within neutron interferometry we performed an experimental test
of the Kochen-Specker theorem with an inequality, which identifies quantum
contextuality, by using spin-path entanglement in a single neutron system. Here
entanglement is achieved not between different particles, but between degrees
of freedom, i.e., between spin and path degree of freedom. Appropriate
combinations of the spin analysis and the position of the phase shifter allow
an experimental verification of the violation of an inequality of the
Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above
the threshold of 1, clearly shows that quantum mechanical predictions cannot be
reproduced by noncontextual hidden variable theories.
