  We study gravitational-wave emission from the quasi-circular, extreme mass
ratio inspiral of compact objects of mass m0 into massive objects of mass M>>m0
whose external metric is identical to the Schwarzschild metric, except for the
absence of an event horizon. To be specific we consider one of the simplest
realizations of such an object: a nonrotating thin-shell gravastar. The power
radiated in gravitational waves during the inspiral shows distinctive peaks
corresponding to the excitation of the polar oscillation modes of the
gravastar. For ultra-compact gravastars the frequency of these peaks depends
mildly on the gravastar compactness. For masses M~10^6Msun the peaks typically
lie within the optimal sensitivity bandwidth of LISA, potentially providing a
unique signature of the horizonless nature of the central object. For
relatively modest values of the gravastar compactness the radiated power has
even more peculiar features, carrying the signature of the microscopic
properties of the physical surface replacing the event horizon.
