Transportation networks are subject to significant travel time uncertainty as a result of traveler behavior, recurring congestion, capacity variability (construction zones, traffic incidents), variation in demand, and so on. Therefore, interest is growing in modeling and optimizing travel time reliability in such networks. This paper proposes an efficient algorithm to compute the path of maximum travel time reliability on a network with normally distributed and correlated link travel times. For this optimal reliability path (ORP) problem, it is shown that the subpath optimality condition for the deterministic shortest path problem does not hold, and consequently, a new bounds-based optimality criterion is proposed using the K shortest expected time paths and the minimum path variance on the network. An algorithm is developed to solve the ORP problem on the basis of the proposed optimality criterion and an efficient path generation procedure. Computational experiments on various test networks show the proposed algorithm to be efficient, requiring limited path enumeration. With as few as five shortest paths and 50 Monte Carlo draws, the proposed algorithm is able to find the most reliable path for realistic network sizes. Empirical investigations highlight the unreliability of the least expected time path and suboptimality of the independence assumption. The study also underscores the role of risk attitudes (reflected by reliability threshold) on the benefits of the ORP. The algorithm and empirical results have important applications for developing reliability-based routing applications for congestion mitigation and intelligent transportation systems.