We demonstrate that rotationally symmetric chiral metasurfaces can support sharp resonances with the maximum optical chirality determined by precise shaping of bound states in the continuum (BICs). Being uncoupled from one circular polarization of light and resonantly coupled to its counterpart, a metasurface hosting the chiral BIC resonance exhibits a narrow peak in the circular dichroism spectrum with the quality factor limited by weak dissipation losses. We propose a realization of such chiral BIC metasurfaces based on pairs of dielectric bars and validate the concept of maximum chirality by numerical simulations.