Double Integrals · Superchallenge problem

Evaluate $\displaystyle\int_0^{1}\!\int_0^{1} \dfrac{1}{1 - xy}\,dx\,dy$. You may use $\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^2} = \dfrac{\pi^2}{6}$. Give an exact answer.