Alfvén waves are considered to be physically important in understanding physical processes in the solar corona such as nonthermal heating, solar wind acceleration and the abundance enhancement of low first-ionization-potential elements. However, it is still not clear how these waves are excited in the lower atmosphere. To reveal their physical origin, we have attempted to detect Alfvénic waves in the solar chromosphere using the spectroscopic method. By analyzing the spectral data taken by the Fast Imaging Solar Spectrograph of the 1.6 meter Goode Solar Telescope, we successfully detected the Alfvénic waves in the superpenumbral fibrils around a sunspot. This is the first spectroscopic detection of Alfvénic waves in the solar chromosphere. These waves are found to be physically associated with the three-minute umbral oscillation. We conclude that the Alfvénic waves excited by the slow-to-Alfvén mode conversion may prevail in the solar chromosphere.