  The Chermak-Delgado lattice of a finite group is a dual, modular sublattice
of the subgroup lattice of the group. This paper considers groups with a
quasi-antichain interval in the Chermak-Delgado lattice, ultimately proving
that if there is a quasi-antichain interval between $L$ and $H$ with $L \leq H$
then there exists a prime $p$ such that the quotient $H / L$ is an elementary
abelian $p$-group and the number of atoms in the quasi-antichain is one more
than a power of $p$. In the case where the Chermak-Delgado lattice of the
entire group is a quasi-antichain, the relationship between the number of
abelian atoms and the prime $p$ is examined; additionally several examples of
group with a quasi-antichain Chermak-Delgado lattice are constructed.
