In this paper, we present a lossless image encryption algorithm utilizing robust chaos based dynamic DNA coding and DNA operations (DNA XOR and DNA Complement). The entire process of encryption is controlled by the pseudo-random number sequences generated through a 1D robust chaos map that exhibits chaotic behaviour in a very large region of parameter space with no apparent periodic window and therefore possesses a fairly large key space. Due to peculiar feed-forward and feedback mechanisms, which modify the synthetic image (created to initiate the encryption process) at the encryption of each pixel, the proposed algorithm possesses extreme sensitivity to the plain image, cipher image and secret key. The performance analysis proves that the proposed algorithm exhibits excellent features (as expected from ideal image encryption algorithms) and is robust against various statistical and cryptanalytic attacks.