The preservation of high peak signal‐to‐noise ratio of the watermarked image is required in some applications. The chaos‐based fragile watermarking proposed by Rawat et al. in 2011 can meet this requirement, for only one LSB plane of the original image is modified by the watermark data. However, there are three drawbacks in the original scheme: (i) insecurity, the host image can be tampered without being detected; (ii) the detected tampered area is incomplete; and (iii) the most important thing is that the tampered area is unrecoverable. Enlightened by the work of Rawat et al., we propose a new recoverable chaos‐based fragile watermarking scheme, in which all of the drawbacks in the original scheme have been overcome, while the size of the watermark is unchanged, therefore the high peak signal‐to‐noise ratio characteristic can be preserved. The chaotic map is used to ensure the security; the idea of block dividing is adopted to improve the tamper detection and to make storage space for the recovery data embedding; and the border matching recovery based on vector quantization is proposed to improve the recovery result of the target image. Experiments show that our method is secure and recoverable, and the recovery ability is extremely satisfactory. Copyright © 2016 John Wiley & Sons, Ltd.