  By exploiting an old idea first used by Pizzetti for the classical Laplacian,
we introduce a notion of {\it asymptotic average solutions} making pointwise
solvable every Poisson equation $\mathcal{L} u(x)=-f(x)$ with continuous data
$f$, where $\mathcal{L}$ is a hypoelliptic linear partial differential operator
with positive semidefinite characteristic form.
