This paper presents a computationally efficient algorithm to compute oblique scattering from a bianisotropic object immersed in a chiral host. The analysis is performed in terms of Beltrami fields, as these form a natural basis for representing waves in a chiral medium. Volume integral equations are derived solely in terms of the axial components of the Beltrami fields and are discretized using pyramidal basis functions. The integral equations are solved iteratively using a fast multipole accelerated method of moments technique with a computational complexity of O(N1.4) per iteration. A windowed translation operator is introduced, which further reduces the computational complexity of the algorithm to O(N1.33). Our numerical results are validated against Mie-type solutions for anisotropic cylinders and shells. Results for scattering from large bianisotropic corrugated surfaces are presented.