While automatic text summarization is an area that has received a great deal of attention in recent research, the problem of efficiency in this task has not been frequently addressed. When the size and quantity of documents available on the Internet and from other sources are considered, the need for a highly efficient tool that produces usable summaries is clear. We present a linear-time algorithm for lexical chain computation. The algorithm makes lexical chains a computationally feasible candidate as an intermediate representation for automatic text summarization. A method for evaluating lexical chains as an intermediate step in summarization is also presented and carried out. Such an evaluation was heretofore not possible because of the computational complexity of previous lexical chains algorithms.