Scattering by a three-dimensional object composed of a chiral medium (the interior medium) and immersed in a simple Lorentz-nonreciprocal medium with magnetoelectric gyrotropy (the exterior medium) was treated using the extended boundary condition method (EBCM). The exterior medium is quantified by εre, μre, and Γ, whereas the interior medium is quantified by εri, μri, and β. When irradiated by a plane wave, the differential scattering efficiency does not depend on the polarization state of the incident plane wave if the exterior medium is impedance-matched with the interior medium, regardless of the shape of the object, Γ, and β. Zero backscattering is possible if, in addition to impedance-matching condition, the object is rotationally symmetric about the propagation direction, and Γ is parallel to the propagation direction. Numerical results confirm these remarks for scattering by spheroids. On fixing εri, μri, εre, and μre, the effects of Γ and β on the total scattering efficiency were examined for a sphere. The total scattering efficiency does not depend on the polarization state of the incident plane wave, even when the exterior medium is not impedance-matched with the interior medium, and despite the presence of Γ and β. The total scattering efficiency when Γ is coparallel to the propagation direction can be either equal to, larger than, or smaller than when Γ is antiparallel or perpendicular to the propagation direction, depending on β and the electrical size of the sphere. It is found that parallel propagation of the incident plane wave with respect to Γ has a stronger influence than perpendicular propagation, regardless of β and the electrical size of the sphere. The effect of increasing/decreasing the magnitude of Γ can be envisioned only when its direction is parallel to the propagation direction.