Nowadays, text encryption is recommendable when it is transmitted or stored on insecure channels as Internet. By the other hand, the chaotic systems have excellent characteristics as mixing data, ergodicity, sensitivity to initial conditions, and control parameters, etc., all them useful to design cryptographic algorithms with big size keys and an efficient permutation–diffusion process. In this work, we present a novel symmetric text cipher algorithm based on chaos; we use a 128 bit secret key, two logistic maps with optimized pseudorandom sequences, plain text characteristics, and only one permutation–diffusions round. Several security analysis are presented as secret key size, secret key sensitivity, frequency with histograms, autocorrelation analysis, information entropy analysis, differential analysis, classic attacks analysis, and encryption/decryption time. Based in numerical simulation results, the proposed encryption algorithm presents high security, an excellent encryption time, and it can resist a powerful chosen/known plain text attack; therefore, it can be implemented in real-time applications.