  More than a quarter century after the discovery of the high temperature
superconductor (HTS) YBa$_2$Cu$_3$O$_{6+\delta}$ (YBCO) studies continue to
uncover complexity in its phase diagram. In addition to HTS and the pseudogap
there is growing evidence for multiple phases with boundaries which are
functions of temperature ($T$), doping (p) and magnetic field. Here we report
the low temperature electronic specific heat (C$_{elec}$) of YBCO6.47 (p=0.08)
up to a magnetic field (H) of 34.5 teslas (T), a poorly understood region of
the underdoped H-$T$-p phase space. We observe two regimes: below a
characteristic magnetic field H'$\approx$10 T, C$_{elec}/T$ obeys an expected
H$^{1/2}$ behavior, however, near H' there is a sharp inflection followed by a
linear-in-H behavior. H' rests deep within the superconducting phase and the
linear-in-H behavior is observed in the zero resistance regime. In the limit of
zero temperature, C$_{elec}/T$ is proportional to the zero-energy electronic
density of states. Thus this inflection is evidence of a magnetic-field-driven
quantum phase transition.
