  We consider a single Rouse polymer chain in two dimensions in presence of a
transverse shear flow along the $x$ direction and calculate the persistence
probability $P_0(t)$ that the $x$ coordinate of a bead in the bulk of the chain
does not return to its initial position up to time $t$. We show that the
persistence decays at late times as a power law, $P_0(t)\sim t^{-\theta}$ with
a nontrivial exponent $\theta$. The analytical estimate of $\theta=0.359...$
obtained using an independent interval approximation is in excellent agreement
with the numerical value $\theta\approx 0.360\pm 0.001$.
