Periodically chirped sampled fiber Bragg gratings (PC-SFBGs) are proposed as multichannel comb filters. A PC-SFBG consists of many chirp periods corresponding to the periodic chirp effect. With the same chirp coefficient released for a linearly chirped SFBG (LC-SFBG), the spectral self-imaging phenomenon is also observed in the PC-SFBG. Compared with a uniform SFBG, the PC-SFBG exhibits a narrower channel spacing and a similar group-delay characteristic in the reflection bands. Meanwhile, the PC-SFBG ensures a more accurate phase-shift condition (or a better tolerance on the chirp coefficient) and higher peak reflectivities than the LC-SFBG.