Stream ciphers are essential tools for encrypting sensitive data. While having the limitation that a single key may never be used twice, they are often very fast and can offer a valuable alternative to block ciphers in many applications. In this contribution we describe a novel stream cipher based on discrete Kolmogorov systems. Based on a theorem stating that discrete Kolmogorov systems can provide a perfect permutation operator, we develop a strong generator for pseudo-random bits or bytes. These bits or bytes are then added to the plaintext stream to produce the desired ciphertext stream in a straightforward manner.