  This short paper is concerned with polynomial Pell equations \[P^2-DQ^2=1,\]
with $P,Q,D\in\Bbb C[X]$ and ${deg}(D)=2$. The main result shows that the
polynomials $P$ and $Q$ are closely related to Chebyshev polynomials. We then
investigate the existence of such polynomials in $\Bbb Z[X]$ specializing to
fixed solutions of ordinary Pell equations over the integers.
