We present the first results of the holographic beam mapping program for the Canadian Hydrogen Intensity Mapping Experiment (CHIME). We describe the implementation of the holographic technique as adapted for CHIME, and introduce the processing pipeline which prepares the raw holographic timestreams for analysis of beam features. We use data from six bright sources across the full 400-800\,MHz observing band of CHIME to provide measurements of the co-polar and cross-polar beam response of CHIME in both amplitude and phase for the 1024 dual-polarized feeds instrumented on CHIME. In addition, we present comparisons with independent probes of the CHIME beam which indicate the presence of polarized beam leakage in CHIME. Holographic measurements of the CHIME beam have already been applied in science with CHIME, e.g. in estimating detection significance of far sidelobe FRBs, and in validating the beam models used for CHIME's first detections of \tcm emission (in cross-correlation with measurements of large-scale structure from galaxy surveys and the Lyman- forest). Measurements presented in this paper, and future holographic results, will provide a unique data set to characterize the CHIME beam and improve the experiment's prospects for a detection of BAO.