  Many-body methods that use Gaussian-wave packets to describe nucleon-spatial
distribution have been widely employed for depicting various phenomena in
nuclear systems, in particular clustering. So far, however, the chiral
effective field theory, a state-of-the-art theory of nuclear force, has not
been applied to such methods. In this paper, we give the formalism to calculate
the two-body matrix elements of the chiral two-nucleon forces using the
Gaussian-wave packets. We also visualize the matrix elements and investigate
the contributions of the central and tensor forces. This work is a foothold
towards an \textit{ab initio} description of various cluster phenomena in view
of nucleons, pions, and many-nucleon forces.
