Quasi-bound states in the continuum (q-BICs) are resonant states of suitably tailored nanostructures with long optical lifetimes controlled by symmetry-breaking perturbations. While in planarized ultrathin devices the resulting Fano resonance is limited to linear polarizations, we show here that chiral perturbations extend q-BIC concepts to arbitrary elliptical polarizations. Using geometric phase engineering, we realize metasurfaces with ultrasharp Fano spectral features that can shape the impinging wavefront with near-unity efficiency, while at the same time precisely filtering their spectral content.