We obtain stringent constraints on near-horizon deviations of a black hole from the Kerr geometry by performing a long-duration Bayesian analysis of the gravitational-wave data immediately following GW150914. GW150914 was caused by a binary system that merged to form a final compact object. We parameterize deviations of this object from a Kerr black hole by modifying its boundary conditions from full absorption to full reflection, thereby modeling it as a horizonless ultracompact object. Such modifications result in the emission of long-lived monochromatic quasinormal modes after the merger. These modes would extract energy on the order of a few solar masses from the final object, making them observable by LIGO. By putting bounds on the existence of these modes, we show that the Kerr geometry is not modified down to distances as small as $4 times 10^{-16}$ meters away from the horizon. Our results indicate that the post-merger object formed by GW150914 is a black hole that is well described by the Kerr geometry.
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