It is still a mystery how the solar chromosphere can stand high above the photosphere. The dominant portion of this layer must be dynamically supported, as is evident by the common occurrence of jets such as spicules and mottles in quiet regions, and fibrils and surges in active regions. Hence, revealing the driving mechanism of these chromospheric jets is crucial for our understanding of how the chromosphere itself exists. Here, we report our observational finding that fibrils in the superpenumbra of a sunspot are powered by sunspot oscillations. We find patterns of outward propagation that apparently originate from inside the sunspot, propagate like running penumbral waves, and develop into the fibrils. Redshift ridges seen in the time-distance plots of velocity often merge, forming a fork-like pattern. The predominant period of these shock waves increases, often jumping with distance, from 3 minutes to 10 minutes. This short-to-long period transition seems to result from the selective suppression of shocks by the falling material of their preceding shocks. Based on our results, we propose that the fibrils are driven by slow shock waves with long periods that are produced by the merging of shock waves with shorter periods propagating along the magnetic canopy.