The security protocols used in ZigBee rely on an advanced encryption standard-counter mode (AES-CTR) algorithm to encrypt data before transmission. This algorithm is very robust, but it is time consuming. For some industrial and medical applications, it does not meet the real-time requirement. When the AES is used in counter mode CTR, it becomes like a stream cipher that aims to generate pseudorandom bits. Also, to encrypt data, the latter are combined with the plaintext using the XOR operation. New fast stream ciphers were proposed for the eStream project, but these ciphers have shown some weakness. On the other hand, ciphers based on chaotic functions seem to be more promising. Detailed analyses have shown that chaotic functions have very good cryptographic properties and can be used to construct high speed and strong stream ciphers. In this paper, a new robust and fast chaotic encryption algorithm RFCA is presented. This consists of a chaotic cipher composed of two perturbed maps piecewise linear chaotic map. This algorithm is, in particular, adequate for data encryption in ZigBee networks where robustness and real time are both essential. A comparison between our algorithm (RFCA) and the AES-CTR, the simplified AES, and the eStream finalist candidates, is presented with regard to speed and robustness. This is done using correlation coefficients, unified average changing intensity, number of pixels change rate, and test of randomness for the generated bit sequences using the National Institute of Standards and Technology statistical test suite.