  We present a so far undetected submonolayer phase of copper telluride on
Cu(111) with $\left(5 \times \sqrt{3}\right)_{\text{rect}}$ periodicity and
coverage of 0.40 ML Tellurium (Te), which can be grown with perfect long-range
order. It is structurally characterized by a combination of quantitative
low-energy electron diffraction (LEED-IV), scanning tunneling microscopy (STM),
and density functional theory (DFT). We find that Te induces the formation of
four atom wide linear troughs within the Cu(111) surface filled up by two Te
atoms per unit cell. Additionally, the interspace between the troughs is
decorated by Cu$_2$Te$_2$ ad-chains sitting at hcp sites. All Te atoms exhibit
the same local sixfold coordination: They occupy threefold hollow sites of the
substrate and are one-sided attached to another three Cu atoms. The presented
structural model is verified by a LEED-IV analysis with Pendry R-factor of R =
0.174 and quantitative agreement of structural parameters with DFT predictions.
It also has by far the lowest energy of all models tested by DFT and simulated
STM images agree perfectly with experiment. It turns out that the new $\left(5
\times \sqrt{3}\right)_{\text{rect}}$ phase is the most dense surface telluride
phase possible on Cu(111) before bulk-like copper telluride starts to growth.
