  It has recently been suggested that the organic compound
NiCl$_2$-4SC(NH$_2$)$_2$ (DTN) exhibits Bose-Einstein Condensation (BEC) of the
Ni spin degrees of freedom for fields applied along the tetragonal c-axis. The
Ni spins exhibit 3D XY-type antiferromagnetic order above a field-induced
quantum critical point at $H_{c1} \sim 2$ T. The Ni spin fluid can be
characterized as a system of effective bosons with a hard-core repulsive
interaction in which the antiferromagnetic state corresponds to a Bose-Einstein
condensate (BEC) of the phase coherent $S = 1$ Ni spin system. We have
investigated the the high-field phase diagram and the occurrence of BEC in DTN
by means of specific heat and magnetocaloric effect measurements to dilution
refrigerator temperatures. Our results indicate that a key prediction of BEC is
satisfied; the magnetic field-temperature quantum phase transition line
$H_c(T)-H_{c1} \propto T^\alpha$ approaches a power-law at low temperatures,
with an exponent $\alpha = 1.47 \pm 0.06$ at the quantum critical point,
consistent with the BEC theory prediction of $\alpha = 1.5$.
