  We analyze gravitational-wave data from the first LIGO detection of a binary
black-hole merger (GW150914) in search of the ringdown of the remnant black
hole. Using observations beginning at the peak of the signal, we find evidence
of the fundamental quasinormal mode and at least one overtone, both associated
with the dominant angular mode ($\ell=m=2$), with $3.6\sigma$ confidence. A
ringdown model including overtones allows us to measure the final mass and spin
magnitude of the remnant exclusively from postinspiral data, obtaining an
estimate in agreement with the values inferred from the full signal. The mass
and spin values we measure from the ringdown agree with those obtained using
solely the fundamental mode at a later time, but have smaller uncertainties.
Agreement between the postinspiral measurements of mass and spin and those
using the full waveform supports the hypothesis that the GW150914 merger
produced a Kerr black hole, as predicted by general relativity, and provides a
test of the no-hair theorem at the ${\sim}10\%$ level. An independent
measurement of the frequency of the first overtone yields agreement with the
no-hair hypothesis at the ${\sim 20}\%$ level. As the detector sensitivity
improves and the detected population of black hole mergers grows, we can expect
that using overtones will provide even stronger tests.
