The H alpha line is an important optical line in solar observations containing the information from the photosphere to the chromosphere. To study the mechanisms of solar eruptions and the plasma dynamics in the lower atmosphere, the Chinese H alpha Solar Explorer (CHASE) was launched into a Sun-synchronous orbit on October 14, 2021. The scientific payload of the CHASE satellite is the H alpha Imaging Spectrograph (HIS). The CHASE/HIS acquires, for the first time, seeing-free H alpha spectroscopic observations with high spectral and temporal resolutions. It consists of two observational modes. The raster scanning mode provides full-Sun or region-of-interest spectra at H alpha (6559.7-6565.9 angstrom) and Fe I (6567.8-6570.6 angstrom) wavebands. The continuum imaging mode obtains full-Sun photospheric images at around 6689 angstrom. In this paper, we present detailed calibration procedures for the CHASE/HIS science data, including the dark-field and flat-field correction, slit image curvature correction, wavelength and intensity calibration, and coordinate transformation. The higher-level data products can be directly used for scientific research.