  CaFeAsF is an iron-based superconductor parent compound whose Fermi surface
is quasi-two dimensional, composed of Dirac-electron and Schr\"odinger-hole
cylinders elongated along the $c$ axis. We measured the longitudinal and Hall
resistivities in CaFeAsF with the electrical current in the $ab$ plane in
magnetic fields up to 45 T applied along the $c$ axis and obtained the
corresponding conductivities via tensor inversion. We found that both the
longitudinal and Hall conductivities approached zero above $\sim$40 T as the
temperature was lowered to 0.4 K. Our analysis indicates that the Landau-level
filling factor is $\nu$ = 2 for both electrons and holes at these high field
strengths, resulting in a total filling factor $\nu$ = $\nu_{hole} -
\nu_{electron}$ = 0. We therefore argue that the $\nu$ = 0 quantum Hall state
emerges under these conditions.
