Vaccine hesitancy due to safety concerns is a hindrance to the success of vaccination campaigns. In February 2021, Trinidad and Tobago commenced its National COVID-19 Vaccination Program. Healthcare workers were among the first group to receive the ChAdOx1 nCoV-19 (Oxford-AstraZeneca (Covishield, Serum Institute of India, Pune, India), the first COVID-19 vaccine available nationally. This study examined the safety of this vaccine in terms of the systemic and local adverse events following immunization reported by healthcare worker recipients. A cross-sectional study was conducted via a telephone questionnaire. Data concerning demographics, medical and COVID-19-related anamneses, and local and systemic side effects experienced within the first 48 h after receiving the first and second dose of this vaccine, respectively, were gathered. Among the 687 participants (male = 275; female = 412), prevalence of fever, body pain, chills, nausea, myalgia, headache, malaise, fatigue, and other systemic symptoms declined significantly 48 h after administration of the second dose compared to the first dose. Chi-square test and multiple logistic regression demonstrated the greater likelihood of younger recipients to report systemic symptoms compared to older recipients. Multiple logistic regression indicated that females were more likely to report headache, fatigue, and discomfort, and were less likely to report no symptoms, compared to males, after both doses. On average, recipients reported less local and systemic side effects 48 h after receiving the second dose compared to the first dose. The reported rate of occurrence of side effects was <50% for most adverse events, which is consistent with the manufacturer's claims that the vaccine is safe. This study adds data on the safety of this vaccine in a population that has not been previously studied. The findings can inform public health policy efforts to lower vaccine hesitancy based on safety concerns surrounding the ChAdOx1 nCoV-19 vaccine across various groups in society, including healthcare workers.