A simple and very precise group delay ripple (GDR) measurement technique for linearly chirped fiber Bragg gratings (CFBGs) is proposed. It is based on real-time optical Fourier transformation of an ultrashort pulse directly induced by the CFBG dispersion. We have experimentally demonstrated highly accurate characterization of the GDR profile of a commercial $10\text{-}\mathrm{m}$ -long CFBG with a dispersion of $+2000\mathrm{ps}∕\mathrm{nm}$ , having achieved a remarkably small standard deviation in our measurements of about $4\mathrm{ps}$ over a bandwidth of $28\mathrm{nm}$ . The proposed method has the unique potential to provide real-time GDR monitoring (in the MHz range) by use of commercially available high-speed sampling electronics.