  We say that two sets $S,T\subset\{1,2,\dots,n\}$ are chord separated if there
does not exist a cyclically ordered quadruple $a,b,c,d$ of integers satisfying
$a,c\in S-T$ and $b,d\in T-S$. This is a weaker version of Leclerc and
Zelevinsky's weak separation. We show that every maximal by inclusion
collection of pairwise chord separated sets is also maximal by size. Moreover,
we prove that such collections are precisely vertex label collections of fine
zonotopal tilings of the three-dimensional cyclic zonotope. In our
construction, plabic graphs and square moves appear naturally as horizontal
sections of zonotopal tilings and their mutations respectively.
