We consider the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, to explain how the polymer statistics changes with Weissenberg number, ${\it Wi}$, the product of the polymer relaxation time and the Lyapunov exponent of the flow, $\bar\lambda$. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction, having algebraic tails. The PDF of the tumbling time (separating two subsequent flips), $\tau$, has a maximum estimated as $\bar\lambda^{-1}$. This PDF shows an exponential tail for large $\tau$ and a small-$\tau$ tail determined by the simultaneous statistics of the velocity PDF. Four regimes of ${\it Wi}$ are identified for the extension statistics: one below the coil–stretched transition and three above the coil–stretched transition. Emphasis is given to explaining these regimes in terms of the polymer dynamics.