  The loss of orbital energy and angular momentum to gravitational waves
produced in a binary inspiral forces the orbital eccentricity to adiabatically
evolve and oscillate. For comparable-mass binaries, the osculating eccentricity
is thought to decrease monotonically in the inspiral. Contrary to this, we here
show that, once the osculating eccentricity is small enough, radiation reaction
forces it to grow secularly before the binary reaches the last stable orbit. We
explore this behavior, its physical interpretation and consequences, and its
potential impact on future gravitational wave observations.
