  We study the linear transport equation \[ \frac{\partial}{\partial t} u ( t,x
) +b ( t,x ) \cdot \nabla u ( t,x ) + \nabla u ( t,x ) \cdot
\frac{\partial}{\partial t} X ( t ) =0, \hspace{2em} u ( 0,x ) =u_{0} ( x ) \]
where $b$ is a vectorfield of limited regularity and $X$ a vector-valued
H\"older continuous driving term. Using the theory of controlled rough paths we
give a meaning to the weak formulation of the PDE and solve that equation for
smooth vectorfields $b$. In the case of the fractional Brownian motion a
phenomenon of regularization by noise is displayed.
