Skyline queries represent a powerful tool for multidimensional data analysis and for decision aid. When the dimensions are conflicting, skyline queries return the best compromises associated with these dimensions. Many studies have focused on the extraction of skyline points in the context of multidimensional databases, but, to the best of our knowledge, none of them have investigated skyline queries, when data are structured along multiple and hierarchical dimensions. This article proposes a new method that extends skyline queries to multiple hier- archical dimensions. Our proposal, HSky (Hierarchical Skyline Queries) allows the user to navigate along the dimensions hierarchies (i.e. specialize / generalize) while ensuring an efficient online calculation of the associated skyline.