  We construct a Lagrangian submanifold, inside the cotangent bundle of a real
torus, which we call a Lagrangian pair of pants. It is given as the graph of
the differential of a smooth function defined on the real blow up of a
Lagrangian coamoeba. Lagrangian pairs of pants are the main building blocks in
a construction of smooth Lagrangian submanifolds of $(\mathbb{C}^*)^n$ which
lift tropical subvarieties in $\mathbb{R}^n$. As an example we explain how to
lift tropical curves in $\mathbb{R}^2$ to Lagrangian submanifolds of
$(\mathbb{C}^*)^2$. We also give several new examples of Lagrangian
submanifolds inside toric varieties, some of which are monotone.
