Fear is an adaptive response in the presence of danger. However, when threat is uncertain and continuous, as in the current coronavirus disease (COVID-19) pandemic, fear can become chronic and burdensome. To identify predictors of fear of the coronavirus, we conducted an online survey (N = 439) three days after the World Health Organization declared the coronavirus outbreak a pandemic (i.e., between March 14 and 17, 2020). Fear of the coronavirus was assessed with the newly developed Fear of the Coronavirus Questionnaire (FCQ) consisting of eight questions pertaining to different dimensions of fear (e.g., subjective worry, safety behaviors, preferential attention), and an open-ended question. The predictors included psychological vulnerability factors (i.e., intolerance of uncertainty, worry, and health anxiety), media exposure, and personal relevance (i.e., personal health, risk for loved ones, and risk control). We found four predictors for the FCQ in a simultaneous regression analysis: health anxiety, regular media use, social media use, and risks for loved ones (R = .37). Furthermore, 16 different topics of concern were identified based participants' open-ended responses, including the health of loved ones, health care systems overload, and economic consequences. We discuss the relevance of our findings for managing people's fear of the coronavirus.