  A Cahn-Hilliard equation with stochastic multiplicative noise and a random
convection term is considered. The model describes isothermal phase-separation
occurring in a moving fluid, and accounts for the randomness appearing at the
microscopic level both in the phase-separation itself and in the flow-inducing
process. The call for a random component in the convection term stems naturally
from applications, as the fluid's stirring procedure is usually caused by
mechanical or magnetic devices. Well-posedness of the state system is addressed
and optimisation of a standard tracking type cost with respect to the velocity
control is then studied. Existence of optimal controls is proved and the
G\^ateaux-Fr\'echet differentiability of the control-to-state map is shown.
Lastly, the corresponding adjoint backward problem is analysed, and first-order
necessary conditions for optimality are derived in terms of a variational
inequality involving the intrinsic adjoint variables.
