Chirality has always been a hot research topic because it possesses potential applications in polarization optics, chemical and biosensing. In the previous works, intrinsic chirality has been extensively explored, but its development is limited due to the complexity in fabrication of chiral metamaterials. Therefore, there is an urgent need to simplify fabrication and design of compact devices with chiral response. Extrinsic chirality has shown great potential because it can be realized in nonchiral anisotropic planar structures with low-cost fabrication techniques. In this paper, the extrinsic chirality of biaxial hyperbolic material $\alpha {\text -}{\rm{Mo}}{{\rm{O}}_3}$ with in-plane anisotropy has been investigated. By analyzing the effect of thickness of $\alpha {\text -}{\rm{Mo}}{{\rm{O}}_3}$ film, the angle of incidence, azimuth angle, and wavelength of incidence on the circular dichroism (CD), the maximum CD can reach 0.77. This strong extrinsic chirality of the $\alpha {\text -}{\rm{Mo}}{{\rm{O}}_3}$ film results from the mutual orientation of the $\alpha {\text -}{\rm{Mo}}{{\rm{O}}_3}$ film and the incident light. In addition, $\alpha {\text -}{\rm{Mo}}{{\rm{O}}_3}$ film can still maintain strong extrinsic chirality when the azimuthal angle ranges from approximately 20°-57° and the angle of incidence is from 55°-80°.