  We present the design, implementation and performance of a digital backend
constructed for the Canadian Hydrogen Intensity Mapping Experiment (CHIME) that
uses accelerated computing to observe radio pulsars and transient radio
sources. When operating, the CHIME correlator outputs 10 independent streams of
beamformed data for the CHIME/Pulsar backend that digitally track specified
celestial positions. Each of these independent streams are processed by the
CHIME/Pulsar backend system which can coherently dedisperse, in real-time, up
to dispersion measure values of 2500 pc/cm$^{-3}$ . The tracking beams and
real-time analysis system are autonomously controlled by a priority-based
algorithm that schedules both known sources and positions of interest for
observation with observing cadences as small as one day. Given the distribution
of known pulsars and radio-transient sources, the CHIME/Pulsar system can
monitor up to 900 positions once per sidereal day and observe all sources with
declinations greater than $-20^\circ$ once every $\sim$2 weeks. We also discuss
the science program enabled through the current modes of data acquisition for
CHIME/Pulsar that centers on timing and searching experiments.
