This study considers turnover intention from a stress theory perspective as a coping response to illegitimate tasks. We build on the stress-as-offense-to-self (SOS) framework to analyze the relationship between illegitimate tasks and turnover intention and the moderating role of appreciative leadership as an organizational resource. According to the SOS concept, illegitimate tasks are tasks that are considered unnecessary or unreasonable, thus violating expectations about what can reasonably be required from an employee. They signal a lack of appreciation and respect to the employee, who is expected to fulfill them, and thus constitute a threat to one’s self-esteem. In contrast, perceived appreciative leadership strengthens employees’ self-esteem by praise and acknowledgment. A total of 235 German information technology (IT) professionals of 4 IT companies participated in this study. Results supported the theoretical assumptions that, controlling for job satisfaction, time pressure, and job control, (a) illegitimate tasks are positively related to turnover intention, and (b) appreciative leadership buffers this relationship. That is, if appreciation by the supervisor is high, illegitimate tasks are less strongly related to turnover intention as compared with low appreciation by the supervisor. The significant association between the task-related stressor (illegitimate tasks) and higher turnover intention extends previous research on the stressor-turnover intention relationship. The buffer effect of appreciative leadership highlights the important role of leadership behavior in preventing turnover intention. Supervisors are recommended to appreciate employee’s achievements and qualities and to avoid assigning illegitimate tasks.