Basic principles of implementing the most fundamental computing functions by chaotic elements are described. They provide a theoretical foundation of computer architecture based on a totally new principle other than silicon chips. The fundamental functions are: the logical AND, OR, NOT, XOR, and NAND operations (gates) and bit-by-bit arithmetic operations. Each of the logical operations is realized by employing a single chaotic element. Computer memory can be constructed by combining logical gates. With these fundamental ingredients in hand, it is conceivable to build a simple, fast, yet cost effective, general-purpose computing device. Chaos computing may also lead to dynamic architecture, where the hardware design itself evolves during the course of computation.. The basic ideas are explained by employing a one-dimensional model, specifically the logistic map.