Chiral structures have been widely used in many fields, such as biosensing and analytical chemistry. In this paper, the chiral response of a composite structure consisting of α-MoO3 film and a silver (Ag) metasurface is studied. First, the effect of the thickness of α-MoO3 film on the circular dichroism (CD) is discussed, and it is found that CD can reach 0.93 at a wavelength of 9.6 µm when the thickness of α-MoO3 film is 6.075 µm. To better understand the physical mechanism, we analyze the transverse electric and transverse magnetic wave components in the transmitted wave for the whole structure and each layer. One can see that the strong chirality of the structure is attributed to the polarization conversion of α-MoO3 film and the selective transmissivity of Ag ribbons. In addition, the influence of the filling factor of the Ag ribbons on chirality is also studied. This work combines hyperbolic material α-MoO3 with Ag ribbons to enhance CD. Also, it provides greater freedom in the tuning of chirality. We believe that this work not only deepens the understanding of the chiral response of anisotropic materials, but also gives promise for its applications in the fields of polarization optics and biosensing.