  Exchange interactions between $S=\frac{1}{2}$ sites in piperazinium
hexachlorodicuprate produce a frustrated bilayer magnet with a singlet ground
state. We have determined the field-temperature phase diagram by high field
magnetization and neutron scattering experiments. There are two quantum
critical points: $H_{c1}=7.5$ T separates a quantum paramagnet phase from a
three dimensional, antiferromagnetically-ordered state while $H_{c2}=37$ T
marks the onset of a fully polarized state. The ordered phase, which we
describe as a magnon Bose-Einstein condensate (BEC), is embedded in a quantum
critical regime with short range correlations. A low temperature anomaly in the
BEC phase boundary indicates that additional low energy features of the
material become important near $H_{c1}$.
