Lattice resonances are collective electromagnetic modes
supported
by periodic arrays of metallic nanostructures. These excitations arise
from the coherent multiple scattering between the elements of the
array and, thanks to their collective origin, produce very strong
and spectrally narrow optical responses. In recent years, there has
been significant effort dedicated to characterizing the lattice resonances
supported by arrays built from complex unit cells containing multiple
nanostructures. Simultaneously, periodic arrays with chiral unit cells,
made of either an individual nanostructure with a chiral morphology
or a group of nanostructures placed in a chiral arrangement, have
been shown to exhibit lattice resonances with different responses
to right- and left-handed circularly polarized light. Motivated by
this, here, we investigate the lattice resonances supported by square
bipartite arrays in which the relative positions of the nanostructures
can vary in all three spatial dimensions, effectively functioning
as 2.5-dimensional arrays. We find that these systems can support
lattice resonances with almost perfect chiral responses and very large
quality factors, despite the achirality of the unit cell. Furthermore,
we show that the chiral response of the lattice resonances originates
from the constructive and destructive interference between the electric
and magnetic dipoles induced in the two nanostructures of the unit
cell. Our results serve to establish a theoretical framework to describe
the optical response of 2.5-dimensional arrays and provide an approach
to obtain chiral lattice resonances in periodic arrays with achiral
unit cells.