We propose a simple method to perform real-time measurements of circular dichroism (CD), which suppresses the artifacts introduced by anisotropic samples and nonideal optical elements in conventional spectrometers. A single polarization holographic grating is adopted, whose first orders of diffraction have amplitudes that are proportional to the right and left circular polarization component of the input light. We demonstrate that, exploiting unpolarized white light and the intrinsic spectral selectivity of the grating, the true CD spectrum is evaluated in parallel in the spectral range of interest from the intensities of the two diffraction orders, I(+1) and I(-1).