  We consider free multiple stochastic measures in the combinatorial framework
of the lattice of all diagonals of an n-dimensional space. In this free case,
one can restrict the analysis to only the noncrossing diagonals. We give
definitions of what free multiple stochastic measures are, and calculate them
for the free Poisson and free compound Poisson processes. We also derive
general combinatorial It\^{o}-type relationships between free stochastic
measures of different orders. These allow us to calculate, for example, free
Poisson-Charlier polynomials, which are the orthogonal polynomials with respect
to the free Poisson measure.
