  In 1967 Wolk proved that every well partial order (wpo) has a maximal chain;
that is a chain of maximal order type. (Note that all chains in a wpo are
well-ordered.) We prove that such maximal chain cannot be found computably, not
even hyperarithmetically: No hyperarithmetic set can compute maximal chains in
all computable wpos. However, we prove that almost every set, in the sense of
category, can compute maximal chains in all computable wpos.
  Wolk's original result actually shows that every wpo has a strongly maximal
chain, which we define below. We show that a set computes strongly maximal
chains in all computable wpo if and only if it computes all hyperarithmetic
sets.
