High quality HgCr$_2$Se$_4$ single crystals have been investigated by magnetization, electron transport and Andreev reflection spectroscopy. In the ferromagnetic ground state, the saturation magnetic moment of each unit cell corresponds to an integer
number of electron spins (3 $mu_B$/Cr$^{3+}$), and the Hall effect measurements suggest n-type charge carriers. Spin polarizations as high as $97%$ were obtained from fits of the differential conductance spectra of HgCr$_2$Se$_4$/Pb junctions with the modified Blonder-Tinkham-Klapwijk (BTK) theory. The temperature and bias-voltage dependencies of the sub-gap conductance are consistent with recent theoretical calculations based on spin active scatterings at a superconductor/half metal interface. Our results suggest that n-HgCr$_2$Se$_4$ is a half metal, in agreement with theoretical calculations that also predict undoped HgCr$_2$Se$_4$ is a magnetic Weyl semimetal.
