Introduction: Considering the global prevalence of coronavirus disease 2019 (COVID-19), a vaccine is being developed to control the disease as a complementary solution to hygiene measures—and better, in social terms, than social distancing. Given that a vaccine will eventually be produced, information will be needed to support a potential campaign to promote vaccination. Objective: The aim of this study was to determine the variables affecting the likelihood of refusal and indecision toward a vaccine against COVID-19 and to determine the acceptance of the vaccine for different scenarios of effectiveness and side effects. Materials and Methods: A multinomial logistic regression method based on the Health Belief Model was used to estimate the current methodology, using data obtained by an online anonymous survey of 370 respondents in Chile. Results: The results indicate that 49% of respondents were willing to be vaccinated, with 28% undecided or 77% of individuals who would potentially be willing to be inoculated. The main variables that explained the probability of rejection or indecision were associated with the severity of COVID-19, such as, the side effects and effectiveness of the vaccine; perceived benefits, including immunity, decreased fear of contagion, and the protection of oneself and the environment; action signals, such as, responses from ones' family and the government, available information, and specialists' recommendations; and susceptibility, including the contagion rate per 1,000 inhabitants and relatives with COVID-19, among others. Our analysis of hypothetical vaccine scenarios revealed that individuals preferred less risky vaccines in terms of fewer side effects, rather than effectiveness. Additionally, the variables that explained the indecision toward or rejection of a potential COVID-19 vaccine could be used in designing public health policies. Conclusions: We discovered that it is necessary to formulate specific, differentiated vaccination-promotion strategies for the anti-vaccine and undecided groups based on the factors that explain the probability of individuals refusing or expressing hesitation toward vaccination.