  We consider the (barotropic) Euler system describing the motion of a
compressible inviscid fluid driven by a stochastic forcing. Adapting the method
of convex integration we show that the initial value problem is ill-posed in
the class of weak (distributional) solutions. Specifically, we find a sequence
$\tau_M \to \infty$ of positive stopping times for which the Euler system
admits infinitely many solutions originating from the same initial data. The
solutions are weak in the PDE sense but strong in the probabilistic sense,
meaning, they are defined on an {\it a priori} given stochastic basis and
adapted to the driving stochastic process.
