We present the data reduction pipeline for CHARIS, a high-contrast integral-field spectrograph for the Subaru Telescope. The pipeline constructs a ramp from the raw reads using the measured nonlinear pixel response, and reconstructs the data cube using one of three extraction algorithms: aperture photometry, optimal extraction, or $chi^2$ fitting. We measure and apply both a detector flatfield and a lenslet flatfield and reconstruct the wavelength- and position-dependent lenslet point-spread function (PSF) from images taken with a tunable laser. We use these measured PSFs to implement a $chi^2$-based extraction of the data cube, with typical residuals of ~5% due to imperfect models of the undersampled lenslet PSFs. The full two-dimensional residual of the $chi^2$ extraction allows us to model and remove correlated read noise, dramatically improving CHARIS performance. The $chi^2$ extraction produces a data cube that has been deconvolved with the line-spread function, and never performs any interpolations of either the data or the individual lenslet spectra. The extracted data cube also includes uncertainties for each spatial and spectral measurement. CHARIS software is parallelized, written in Python and Cython, and freely available on github with a separate documentation page. Astrometric and spectrophotometric calibrations of the data cubes and PSF subtraction will be treated in a forthcoming paper.
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