In this paper, we propose a new scheme which performs both lossless compression and encryption of data. The lossless compression is based on the arithmetic coding (AC) and the encryption is based on a pseudo random bit generator (PRBG). Thus, the plaintext is compressed with a binary arithmetic coding (BAC) whose two mapping intervals are swapped randomly by using a PRBG. In this paper, we propose a PRBG based on the standard chaotic map and the Engel Continued Fraction (ECF) map to generate a keystream with both good chaotic and statistical properties. To be used in cryptography, a PRBG may need to meet stronger requirements than for other applications. In particular, various statistical tests can be applied to the outputs of such generators to conclude whether the generator produces a truly random sequence or not. The numerical simulation analysis indicates that the proposed compression and encryption scheme satisfies highly security with no loss of the BAC compression efficiency.