The Building Block Hypothesis suggests that Genetic Algorithms (GAs) are well-suited for hierarchical problems, where efficient solving requires proper problem decomposition and assembly of solution from sub-solution with strong non-linear interdependencies. The paper proposes a hill-climber operating over the building block (BB) space that can efficiently address hierarchical problems. The new Building Block Hill-Climber (BBHC) uses past hill-climb experience to extract BB information and adapts its neighborhood structure accordingly. The perpetual adaptation of the neighborhood structure allows the method to climb the hierarchical structure solving successively the hierarchical levels. It is expected that for fully non deceptive hierarchical BB structures the BBHC can solve hierarchical problems in linearithmic time. Empirical results confirm that the proposed method scales almost linearly with the problem size thus clearly outperforms population based recombinative methods.