  We model the inspiral of a compact object into a more massive black hole
rotating very near the theoretical maximum. We find that once the body enters
the near-horizon regime the gravitational radiation is characterized by a
constant frequency, equal to (twice) the horizon frequency, with an
exponentially damped profile. This contrasts with the usual "chirping" behavior
and, if detected, would constitute a "smoking gun" for a near-extremal black
hole in nature.
