  We consider the evolution of a supermassive black hole binary (SMBHB)
surrounded by a retrograde accretion disk. Assuming the disk is exactly in the
binary plane and transfers energy and angular momentum to the binary via direct
gas accretion, we calculate the time evolution of the binary's semi-major axis
$a$ and eccentricity $e$. Because the gas is predominantly transferred when the
binary is at apocenter, we find the eccentricity grows rapidly while
maintaining constant $a(1+e)$. After accreting only a fraction of the
secondary's mass, the eccentricity grows to nearly unity; from then on,
gravitational wave emission dominates the evolution, preserving constant
$a(1-e)$. The high-eccentricity waveforms redistribute the peak gravitational
wave power from the nHz to $\mu$Hz bands, substantially affecting the signal
that might be detected with pulsar timing arrays. We also estimate the torque
coupling binaries of arbitrary eccentricity with obliquely aligned circumbinary
disks. If the outer edge of the disk is not an extremely large multiple of the
binary separation, retrograde accretion can drive the binary into the
gravitational wave-dominated state before these torques align the binary with
the angular momentum of the mass supply.
