Italy was the first European country to be affected by the 2019 coronavirus epidemic (COVID-19). Several studies have shown the risk of developing depression, anxiety, and post-traumatic stress disorder in medical and paramedical staff. Causes included the high contagiousness of the virus, the fear of contracting it, the lack of adequate personal protective equipment, and physical and psychological fatigue. In this context, resilience represents a protective factor against adversity and stress burden. The aim of this research was to investigate if and how the resilience and personality profile is able to influence the response to stress and anxiety on a sample of Italian healthcare workers, during the COVID-19 outbreak. The sample consisted of 152 frontline healthcare workers, physicians, and paramedical professionals. Participants completed the online questionnaire measuring the Resilience Scale for Adults, the Big Five Inventory-10 Item, the State Anxiety Inventory, and the Perceived Stress Scale. Analyses of data aimed to show differences in the stress of healthcare workers due to gender and professional role, and at finding, by means of multidimensional scaling, the relations among anxiety, stress, resilience, and traits of personality. The findings gave some suggestions for implementing strategies useful to increase the resilience in healthcare workers and support them to cope with stressful events, typical of the pandemic emergency.