  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-$\alpha$ 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.
