What factors affect a scientist's choice of research problem? Qualitative research in the history, philosophy, and sociology of science suggests that this choice is shaped by an "essential tension" between the professional demand for productivity and a conflicting drive toward risky innovation. We examine this tension empirically in the context of biomedical chemistry. We use complex networks to represent the evolving state of scientific knowledge, as expressed in publications. We then define research strategies relative to these networks. Scientists can introduce novel chemicals or chemical relationships--or delve deeper into known ones. They can consolidate existing knowledge clusters, or bridge distant ones. Analyzing such choices in aggregate, we find that the distribution of strategies remains remarkably stable, even as chemical knowledge grows dramatically. High-risk strategies, which explore new chemical relationships, are less prevalent in the literature, reflecting a growing focus on established knowledge at the expense of new opportunities. Research following a risky strategy is more likely to be ignored but also more likely to achieve high impact and recognition. While the outcome of a risky strategy has a higher expected reward than the outcome of a conservative strategy, the additional reward is insufficient to compensate for the additional risk. By studying the winners of 137 different prizes in biomedicine and chemistry, we show that the occasional "gamble" for extraordinary impact is the most plausible explanation for observed levels of risk-taking. Our empirical demonstration and unpacking of the "essential tension" suggests policy interventions that may foster more innovative research.