Many financial markets operate as electronic limit order books under a price-time priority rule. In this setting, among all resting orders awaiting trade at a given price, earlier orders are prioritized for matching with contra-side liquidity takers. This creates a technological arms race among high-frequency traders and other automated market participants to establish early (and hence advantageous) positions in the resulting first-in-first-out (FIFO) queue. We develop a model for valuing orders based on their relative queue position that incorporates both economic (informational) and stochastic modeling (queueing) aspects. Our model identifies two important components of positional value: (i) a static component that relates to the trade-off at an instant of trade execution between earning a spread and incurring adverse selection costs, and incorporates the fact that adverse selection costs are increasing with queue position; (ii) a dynamic component, that captures the optionality associated with the future value that accrues by locking in a given queue position. Our model offers predictions of order value at different positions in the queue as a function of market primitives, and can be empirically calibrated. We validate our model by comparing it with estimates of queue value realized in backtesting simulations and find the predictions to be accurate. Moreover, for some large tick-size stocks, we find that queue value can be of the same order of magnitude as the bid-ask spread. This suggests that accurate valuation of queue position is a necessary and important ingredient in considering optimal execution or market-making strategies for such assets.