A new highly secure symmetric stream ciphering technique based on hopping of chaotic maps and orbits is introduced in this paper. The chaotic logistic and quadratic maps are used to generate the cipher, while the tent map is used to generate the map hopping sequence. The key determines the initial conditions, orbits, and orbit hopping patterns. There are eight cipher-generating maps. Each map has sixteen orbits. The stream cipher is produced by hopping between both maps and orbits. Detailed examples are provided. The results show that this technique is highly promising.