  Two-dimensional electronic flat bands and their induced correlated electronic
interactions have been discovered, probed, and tuned in interlayer regions of
hexagonally shaped van der Waals moire superlattices. Fabrication of
anisotropic one-dimensional correlated bands by moire interference of 2D,
however, remains a challenge. Here, we report an experimental discovery of 1D
electronic flat bands near the Fermi level in an anisotropic rectangular moire
superlattice composed of in situ grown, vdW stacked two-atomic-layer thick
Bi(110) well-aligned on a SnSe(001) substrate. The epitaxial lattice mismatch
between the aligned Bi and SnSe zigzag atomic chains causes strong
three-dimensional anisotropic atomic relaxations with associated
one-dimensional out-of- and in-plane strain distributions that are expressed in
electronic bands of the Bi(110) layer, which are characterized jointly by
scanning probe microscopy and density functional theory. At the regions of the
strongest out-of-plane shear strain, a series of 1D flat bands near the Fermi
level are experimentally observed and defined in our calculations. We establish
that 1D flat bands can arise in moir\'e superlattices in absence of the
relative layer twist, but solely through the lattice strain. We generalize the
strategy of utilizing strain in lattice mismatched rectangular hetero-bilayers
for engineering correlated anisotropic electronic bands.
