  A fluctuation theory and, in particular, a theory of scale functions is
developed for upwards skip-free L\'evy chains, i.e. for right-continuous random
walks embedded into continuous time as compound Poisson processes. This is done
by analogy to the spectrally negative class of L\'evy processes -- several
results, however, can be made more explicit/exhaustive in our compound Poisson
setting. In particular, the scale functions admit a linear recursion, of
constant order when the support of the jump measure is bounded, by means of
which they can be calculated -- some examples are considered.
