The design of a bit-serial optical computer is described. The central components are LiNb03 directional couplers as logic elements, and fiber optic delay lines as memory elements. The key device characteristics are discussed, including the special properties and limitations that are important when designing with them. Following this the key design issues are addressed. These include computation in a realm where propagation delays are much greater than logic delays, and implementation of circuits without flip-flops. Design principles are exemplified by the design of a n-bit counter. Following this, the design for a simple bit-serial computer is described.