This paper introduces the concept of 'hyper-ambition' in academia as a contributing factor to what has been termed a 'replication crisis' across some sciences. The replication crisis is an umbrella term that covers a range of 'questionable research practices', from sloppy reporting to fraud. There are already many proposals to address questionable research practices, some of which focus on the values, norms, and motivations of researchers and institutes, and suggest measures to promote research integrity. Yet it is not easy to promote integrity in hyper-competitive academic environments that value high levels of ambition. I argue that in such contexts, it is as likely that a kind of hyper-ambition is fostered that (inadvertently or otherwise) prioritises individual success above all, including to the detriment of scientific quality. In addition, efforts to promote values like integrity falter because they rely on sufficient uniformity in motivations or tendencies. Codes and guidance promoting integrity are, however, likely to influence those for whom such values are not optional, while others simply find ways around them. To demonstrate this I offer a thought experiment in which we consider the imaginary working situations of two ordinary academics. I conclude that tackling questionable research practices in the light of the replication crisis requires robust 'top down' measures that expect and accommodate a broader range of academic values, motivations, and tendencies, while challenging those that help to promote hyper-ambition.