Synthetic biology has many valuable applications, but it also gives rise to certain risks. In this paper I discuss the risk of bioterrorism, which often attracts attention in both the mass media and scientific debate, as well as in government reports. While some authors argue that there is a significant risk of bioterrorism connected to synthetic biology, other scholars claim that the risk is exaggerated and that actors often have motives for overstating the risk. In this paper, I argue that some estimates of the risk may be overstated but that certain risks of bioterrorism, such as the creation and spread of known pathogenic viruses, need to be taken seriously. Actors may also have scientific and financial motives for understating the risk. Such understatements are sometimes based on a principle of hope, which says that technological progress is important for the future welfare of humanity and that too much precaution would have bad consequences. I argue that this principle is problematic as the burdens and benefits of synthetic biology may not be equally divided between different social groups. Instead, I claim that the principle of precaution is more justified as a point of departure for assessing advancements within synthetic biology. It tells us that we need strong evidence that such advancements are safe, because there is a potential risk that they may make it easier for terrorist groups to create and spread known pathogenic viruses.