Building public trust and willingness to vaccinate against COVID-19 is as important as developing an effective vaccine. However, a significant minority of the public are unwilling or hesitant to take a COVID-19 vaccine, when available. A nationally representative sample survey (N = 1040) was conducted in July 2020 in New Zealand to identify factors associated with COVID-19 vaccine intention. A 14-item general vaccine hesitancy scale was tested and found to be significantly associated with COVID-19 vaccine intention. A communication campaign from trusted scientific experts, with information that addresses prevailing concerns about vaccines, is likely to help increase COVID-19 vaccine uptake.