Costless pre-play communication has been found to effectively facilitate coordination and enhance efficiency in games with Pareto-ranked equilibria. We report an experiment in which two groups compete in a weakest-link contest by expending costly efforts. Allowing intra-group communication leads to more aggressive competition and greater coordination than control treatments without any communication. On the other hand, allowing inter-group communication leads to less destructive competition. As a result, intra-group communication decreases while inter-group communication increases payoffs. Our experiment thus provides an example of an environment where communication can either enhance or damage efficiency. This contrasts sharply with experimental findings from public goods and other coordination games, where communication always enhances efficiency and often leads to socially optimal outcomes.