When two inventors file patent applications with overlapping, or "interfering" claims, the U.S. patent rights are awarded to the applicant who establishes priority of invention. Patent interference cases are litigated at the U.S. Patent and Trademark Office's Board of Patent Appeals and Interferences. The cases offer a unique window into competition between firms in research and innovation. This paper analyzes a random sample of interferences to investigate the impact of patent policies on innovation strategies. Our results contribute to the policy debate over the appropriate scope of patents and the revision of the U.S. patent priority structure. We find that while interference cases are in general rare, they are highly concentrated among chemical and biomedical firms. Biotechnology patent applications are so likely to be subject to interference litigation that a question arises about their character: a high rate of interfering means that multiple researchers are chasing a large patent prize associated with a well-defined research topic. This in turn suggests that either the scope of biotechnology patents is too broad or the bar for obviousness has been set too low. Alternatively, the benefits of competition and patent racing to innovation are clear in the patent filing behavior of incumbent and challenger firms. Our empirical results suggest that incumbent firms delay filing patent applications relative to challengers, consistent with the hypothesis that incumbents attempt to delay the introduction of new technologies. But competition from an interference challenge leads incumbents to accelerate filing their patent applications, and thus both the commercialization of new technology and the diffusion of technological information. Strategic filing is exacerbated by the unique U.S. priority structure, which awards disputed patent rights to an inventor who proves that he or she is first-to-invent rather than first to file. Reforming the priority structure, a goal of current efforts to harmonize U.S. patent policies with other countries, has been controversial because of its alleged benefits to entrepreneurs. We find no evidence for the claim that the system benefits small firms or individual inventors over large organizations with patent filing expertise. Instead, we find that the system empowers incumbent firms who seek to delay filing their patent applications, knowing that if they lose the race to the patent office they can still obtain the intellectual property rights with a first-to-invent showing.