  We demonstrate theoretically that the shot noise produced by a tunnel barrier
in a two-channel conductor violates a Bell inequality. The non-locality is
shown to originate from entangled electron-hole pairs created by tunneling
events -- without requiring electron-electron interactions. The degree of
entanglement (concurrence) equals 2(T_1 T_2)^1/2 (T_1+T_2)^-1, with T_1,T_2 <<
1 the transmission eigenvalues. A pair of edge channels in the quantum Hall
effect is proposed as experimental realization.
