In accordance with the invention, a continuously chirped fiber Bragg grating is made by fabricating a continuously chirped phase mask and using the mask to write a Bragg grating on a parallel fiber. The chirped phase mask is made by exposing a photoresist-coated mask substrate to two interfering beams: one a collimated beam and the other a beam reflected from a continuously curved mirror. After etching, the resulting phase mask can be used to write a chirped fiber grating having a continuously varying grating period without physical modification of the fiber. The resulting fiber grating has a widened bandwidth and uniform dispersive delay characteristics useful for dispersion compensation in critical telecommunications applications.