The task of finding _Hierarchical_ Heavy Hitters (HHH) was introduced by Cormode et al. [VLDB 2003] as a generalisation of the heavy hitter problem. While finding HHH in data streams has been studied extensively, the question of releasing HHH when the underlying data is private remains unexplored. In this paper, we study differentially private HHH release in both the streaming and non-streaming setting. In the non-streaming setting, we show the surprising result that the relative error in estimating the residual count for any prefix is independent of the height of the hierarchy and the number of heavy hitters in the stream. Meanwhile, in the streaming setting, although the exact version of HHH has low global sensitivity (as counting queries are 1-sensitive), the approximation functions due to streaming have high global sensitivity, linear in the available space. Despite this obstacle, we show that the absolute error for estimating frequencies in the steaming setting is independent of the available space.