Many chiral absorbers have been proposed to obtain selective absorption for left circularly polarized (LCP) and right circularly polarized (RCP) waves. However, it is difficult to realize tunable chiral absorbers with the chiral response for the incidence angle in a wide range. Here we show that a strong chiral response can be realized by using a simple structure composed of a uniaxial slab and a silver grating. The numerical results show that the absorptance of the proposed structure for incidence of LCP wave can be close to unity while the absorptance for incidence of RCP wave can stay close to zero at the resonance wavelength of magnetic polaritons (MPs) in the grating grooves. More importantly, the circular dichroism (CD) of the structure is shown to remain larger than 0.7 for all azimuthal angles and for the incidence angle from 0o up to 30o. In addition, this structure can also be engineered to work in broadband or in different wavelength ranges. Owing to its simple configuration, this device holds promise for polarization-sensitive surface photochemistry and chiral bolometers.