  We build a four-dimensional quaternion-parametrized conformal field theory
(QCFT) using quaternion holomorphic functions as the generators of quaternionic
conformal transformations. Taking the two-dimensional complex-parametrized
conformal field theory (CCFT) as our model, we study the stress tensor, the
conserved charge, the symmetry generators, the quantization conditions and
several operator product expansions (OPE's). Future applications also are
addressed.
