  By using bulk magnetization, electron spin resonance (ESR), heat capacity,
and neutron scattering techniques, we characterize the thermodynamic and
quantum phase diagrams of Ba$_3$Cr$_2$O$_8$. Our ESR measurements indicate that
the low field paramagnetic ground state is a mixed state of the singlet and the
S$_z$ = 0 triplet for $H \perp c$. This suggests the presence of an intra-dimer
Dzyaloshinsky-Moriya (DM) interaction with a DM vector perpendicular to the
c-axis.
