Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. Structures made of nano-scale chiral elements can display chiroptical effects, such as dichroism for left- and right- handed circularly polarized light, which makes them of high interest for applications ranging from quantum information processing and quantum optics to circular dichroism spectroscopy and molecular recognition. At the same time, strong effects have been challenging to achieve even in synthetic optical media and chiroptical effects for light with normal incidence has been speculated to be prohibited in lossless, thin, quasi-two-dimensional structures. Here, we report on our experimental realization of a giant chiroptical effect in a thin monolithic photonic crystal mirror. Unlike conventional mirrors, our structure selectively reflects only one spin state of light, while preserving its handedness, with a near unity level of circular dichroism. The operational principle of the photonic-crystal mirror relies on Guided Mode Resonance (GMR) with simultaneous excitation of leaky TE and TM Bloch modes in the photonic crystal slab. Such modes are not reliant on the suppression of their radiative losses through the long-range destructive interference and even small areas of the photonic-crystal exhibit robust circular dichroism. Despite its simplicity, the mirror strongly surpasses the performance of earlier reported structures and, contrary to a prevailed notion, demonstrates that near unity reflectivity contrast for the opposite helicities is achievable in a quasi-two-dimensional structure.