  We show that second-generation gravitational-wave detectors at their design
sensitivity will allow us to directly probe the ringdown phase of binary black
hole coalescences. This opens the possibility to test the so-called black hole
no-hair conjecture in a statistically rigorous way. Using state-of-the-art
numerical relativity-tuned waveform models and dedicated methods to effectively
isolate the quasi-stationary perturbative regime where a ringdown description
is valid, we demonstrate the capability of measuring the physical parameters of
the remnant black hole, and subsequently determining parameterized deviations
from the ringdown of Kerr black holes. By combining information from
$\mathcal{O}(5)$ binary black hole mergers with realistic signal-to-noise
ratios achievable with the current generation of detectors, the validity of the
no-hair conjecture can be verified with an accuracy of $\sim 1.5\%$ at $90\%$
confidence.
