In recent years chaos has received a great deal of attention from the researches specialized in communications, signal and image processing. The complexity property of the chaotic signal raised the idea of using such signals in secure communications. Digital image watermarking is a technique mainly developed for copyright protection and image authentication and it can be considered as one application area of the secure communication. In this study, a chaos based digital image watermarking algorithm based on redundant discrete wavelet transform (RDWT) and singular value decomposition (SVD) is proposed. To the best of our knowledge, there do not exist any digital watermarking scheme combining RDWT, SVD and chaos. Robustness and invisibility of the proposed method are improved by using the logistic mapping function to generate a chaotic image matrix serving as the watermark that is used to modify the singular values of the low frequency sub-band of the cover image obtained by applying RDWT. The method is shown to be robust against both the geometrical and image processing attacks and to provide better watermark concealment via computer simulations. Using a chaotic signal as the watermark allows the proposed scheme to meet the security requirements as well.