A novel reversible digital watermarking technique for medical images to achieve high level of secrecy, tamper detection, and blind recovery of the original image is proposed. The technique selects some of the pixels from the host image using chaotic key for embedding a chaotically generated watermark. The rest of the pixels are converted to residues by using the Residue Number System (RNS). The chaotically selected pixels are represented by the polynomial. A primitive polynomial of degree four is chosen that divides the message polynomial and consequently the remainder is obtained. The obtained remainder is XORed with the watermark and appended along with the message. The decoder receives the appended message and divides it by the same primitive polynomial and calculates the remainder. The authenticity of watermark is done based on the remainder that is valid, if it is zero and invalid otherwise. On the other hand, residue is divided with a primitive polynomial of degree 3 and the obtained remainder is appended with residue. The secrecy of proposed system is considerably high. It will be almost impossible for the intruder to find out which pixels are watermarked and which are just residue. Moreover, the proposed system also ensures high security due to four keys used in chaotic map. Effectiveness of the scheme is validated through MATLAB simulations and comparison with a similar technique.