  In multivalley systems, the valley pseudospin offers rich physics going from
encoding of information by its polarization (valleytronics), to exploring novel
phases of matter when its degeneracy is changed. Here, by strain engineering,
we reveal fully valley-polarized quantum Hall (QH) phases in the Pb1-xSnxSe
Dirac system. Remarkably, when the valley energy splitting exceeds the
fundamental band gap, we observe a bipolar QH phase, heralded by the
coexistence of hole and electron chiral edge states at distinct valleys in the
same quantum well. This suggests that spatially overlaid counter-propagating
chiral edge states emerging at different valleys do not interfere with each
other.
