  A symmetrically doped double layer electron system with total filling
fraction $\nu=1/m$ decouples into two even denominator ($\nu=1/2 m$) composite
fermion `metals' when the layer spacing is large. Out-of-phase fluctuations of
the statistical gauge fields in this system mediate a singular attractive
pairing interaction between composite fermions in different layers. A
strong-coupling analysis shows that for any layer spacing $d$ this pairing
interaction leads to the formation of a paired quantum Hall state with a
zero-temperature gap $\Delta(0) \propto 1/d^2$. The less singular in-phase
gauge fluctuations suppress the size of the zero-temperature gap, $\Delta(0)
\propto 1/\left({d^2}{(\ln d)^6}\right)$, but do not eliminate the instability.
