  We present the Fermi-surface map of the spin-chiral bulk states for the
non-centrosymmetric semiconductor BiTeI using de Haas-van Alphen and
Shubnikov-de Haas oscillations. We identify two distinct Fermi surfaces with a
unique spindle-torus-type topology and the non-trivial Berry phases, confirming
the spin chirality with oppositely circulating spin-texture. Near the quantum
limit at high magnetic fields, we find a substantial Zeeman effect with an
effective g-factor of ~ 60 for the Rashba-split Fermi surfaces. These findings
provide clear evidence of strong Rashba and Zeeman coupling in the bulk states
of BiTeI, suggesting that BiTeI is a good platform hosting the spin-polarized
chiral states.
