The Braess Paradox (BP) illustrates an important counterintuitive observation that adding links to a directed transportation network with usage externalities may raise the costs of all users. Research on the BP traditionally focuses on congestible networks. We propose and experimentally test a new and more dramatic version of the BP, where the network exhibits both congestion (negative externalities) and cost-sharing (positive externalities) characteristics. Our design also involves experimental manipulation of choice observability, where players choose routes simultaneously in one condition and sequentially in the other. We report robust behavioral evidence of the BP in both conditions. In nine of 10 sessions in the basic network, subjects coordinated successfully to achieve the welfare-maximizing equilibrium. But once the network was augmented with a new link, coordination failure resulted in a major proportion of subjects switching to a new route, resulting in a 37% average increase in individual travel cost across conditions.