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A notion of entangled Markov chain was introduced by Accardi and Fidaleo inthe context of quantum random walk. They proved that, in the finite dimensionalcase, the corresponding states have vanishing entropy density, but they did notprove that they are entangled.  In the present note this entropy result is extended to the infinitedimensional case under the assumption of finite speed of hopping. Then theentanglement problem is discussed for spin 1/2, entangled Markov chainsgenerated by a binary symmetric channel with hopping probability $1-q$. The vonNeumann entropy of these states, restricted on a sublattice is explicitlycalculated and shown to be independent of the size of the sublattice. This is anew, purely quantum, phenomenon.  Finally the entanglement property between the sublattices ${\calA}(\{0,1,...,N\})$ and ${\cal A}(\{N+1\})$ is investigated using the PPTcriterium. It turns out that, for $q\neq 0,1,{1/2}$ the states are nonseparable, thus truly entangled, while for $q=0,1,{1/2}$, they are separable.

ENTANGLED MARKOV CHAINS GENERATED BY SYMMETRIC CHANNELS