Past research in the field of cryptography has not given much consideration to arithmetic coding as a feasible encryption technique, with studies proving compression-specific arithmetic coding to be largely unsuitable for encryption. Nevertheless, adaptive modelling, which offers a huge model, variable in structure, and as completely as possible a function of the entire text that has been transmitted since the time the model was initialised, is a suitable candidate for a possible encryption-compression combine. The focus of the work presented in this paper has been to incorporate recent results of chaos theory, proven to be cryptographically secure, into arithmetic coding, to devise a convenient method to make the structure of the model unpredictable and variable in nature, and yet to retain, as far as is possible, statistical harmony, so that compression is possible. A chaos-based adaptive arithmetic coding-encryption technique has been designed, developed and tested and its implementation has been discussed. For typical text files, the proposed encoder gives compression between 67.5% and 70.5%, the zero-order compression suffering by about 6% due to encryption, and is not susceptible to previously carried out attacks on arithmetic coding algorithms.