Optical CDMA local area networks allow shared access to a broadcast medium. Every node on the network is assigned an optical orthogonal codeword (OOC) to transmit or receive on. OOCs are designed to be pseudo-orthogonal, i.e., the correlation (and therefore the interference) between pairs of codewords is constrained. This paper demonstrates that the use of optical CDMA does not preclude the need for a media access control (MAC) layer protocol to resolve contention for the shared media. OOCs have low spectral efficiency. As more codewords are transmitted simultaneously, the interference between codewords increases and the network throughput falls. This paper analyzes a network architecture where there is virtually no MAC layer, except for choice of the codeset, and shows that its throughput degrades and collapses under moderate to heavy load. We propose an alternate architecture called interference avoidance where nodes on the network use media access mechanisms to avoid causing interference on the line, thereby improving network throughput. Interference avoidance is analyzed and it is shown that it can provide up to 30% improvement in throughput with low delays and no throughput collapse. We validate our analysis through simulation with realistic network traffic traces.