  Spin-valley locking in the band structure of monolayers of MoS$_2$ and other
group-VI dichalcogenides has attracted enormous interest, since it offers
potential for valleytronic and optoelectronic applications. Such an exotic
electronic state has sparsely been seen in bulk materials. Here, we report
spin-valley locking in a bulk Dirac semimetal BaMnSb$_2$. We find valley and
spin are inherently coupled for both valence and conduction bands in this
material. This is revealed by comprehensive studies using first principle
calculations, tight-binding and effective model analyses, angle-resolved
photoemission spectroscopy and quantum transport measurements. Moreover, this
material also exhibits a stacked quantum Hall effect. The spin-valley
degeneracy extracted from the plateau height of quantized Hall resistivity is
close to 2. This result, together with the observed Landau level spin
splitting, further confirms the spin-valley locking picture. In the extreme
quantum limit, we have also observed a two-dimensional chiral metal at the side
surface, which represents a novel topological quantum liquid. These findings
establish BaMnSb$_2$ as a rare platform for exploring coupled spin and valley
physics in bulk single crystals and accessing 3D interacting topological
states.
