Although young adults are not at great risk of becoming severely ill with COVID-19, their willingness to get vaccinated affects the whole community. Vaccine hesitancy has increased during recent years, and more research is needed on its situational determinants. This paper reports a preregistered experiment (N = 654) that examined whether communicating descriptive social norms - information about what most people do - is an effective way of influencing young people's intentions and reducing their hesitancy to take the COVID-19 vaccine. We found weak support for our main hypothesis that conveying strong (compared to weak) norms leads to reduced hesitancy and stronger intentions. Furthermore, norms did not produce significantly different effects compared to standard vaccine information from the authorities. Moreover, no support was found for the hypothesis that young people are more strongly influenced by norms when the norm reference group consists of other young individuals rather than people in general. These findings suggest that the practical usefulness of signaling descriptive norms is rather limited, and may not be more effective than standard appeals in the quest of encouraging young adults to trust and accept a new vaccine.