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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-valuedH\"older continuous driving term. Using the theory of controlled rough paths wegive a meaning to the weak formulation of the PDE and solve that equation forsmooth vectorfields $b$. In the case of the fractional Brownian motion aphenomenon of regularization by noise is displayed.

Rough linear transport equation with an irregular drift