  $\alpha$-RuCl$_3$ is a leading candidate material for theobservation of
physics related to the Kitaev quantum spin liquid (QSL). By combined
susceptibility, specific-heat, and nuclear-magnetic-resonance measurements, we
demonstrate that $\alpha$-RuCl$_3$ undergoes a quantum phase transition to a
QSL in a magnetic field of 7.5 T applied in the $ab$ plane. We show further
that this high-field QSL phase has gapless spin excitations over a field range
up to 16 T. This highly unconventional result, unknown in either Heisenberg or
Kitaev magnets, offers insight essential to establishing the physics of
$\alpha$-RuCl$_3$.
