Steady increases in natural gas transportation volumes have prompted operators to reevaluate the performance of the existing gas pipeline infrastructure. In order to accomplish an increased transportation capacity, conventional wisdom dictates that adding an additional link or a pipe leg in a gas transportation network should enhance its ability to transport gas. Several decades ago, however, Dietrich Braess challenged this traditional understanding for traffic networks. Braess demonstrated that adding extra capacity could actually lead to reduced network efficiency, congestion, and increased travel times for all drivers in the network (the so-called "Braess Paradox"). The study of such counter-intuitive effects, and the quantification of their impact, becomes a significant priority when a comprehensive optimization of the transportation capacity of operating gas network infrastructures is undertaken. Corroborating the existence of paradoxical effects in gas networks could lead to a significant shift in how network capacity enhancements are approached - challenging the conventional view that improving network performance is a matter of increasing network capacity. In this study, we examine the occurrence of Braess' Paradox in natural gas transportation networks, its impact and potential consequences. We show that paradoxical effects do exist in natural gas transportation networks and derive conditions where it can be expected. We discuss scenarios that can mask the effect and provide analytical developments that may guide the identification of paradoxical effects in larger scale networks.