Protocols that provide reliable communication on top of a network that can lose packets rely on periodically retransmitting packets. The choice of retransmission timeout critically affects system performance. This paper presents a first step toward a theoretical study of the choice of retransmission timeout, based on competitive analysis. In general, competitive analysis compares the performance of an on-line algorithm to the performance of an optimal off-line algorithm, which has access to more information. In this context, the job of an algorithm is to choose the retransmission timeout interval; an off-line algorithm knows the exact message delays, whereas an on-line algorithm knows only upper and lower bounds on the delays. The performance measure of interest is the expected value of a linear combination of the number of packets used and the amount of time elapsed. An on-line algorithm for choosing the retransmission timeout is presented that is optimal with respect to the difference between its performance and that of an optimal off-line algorithm. The algorithm is also analyzed with respect to the ratio of its performance and that of an optimal off-line algorithm.