  This paper proves that every projective toric variety is the fine moduli
space for stable representations of an appropriate bound quiver. To accomplish
this, we study the quiver $Q$ with relations $R$ corresponding to the
finite-dimensional algebra $\bigl(\bigoplus_{i=0}^{r} L_i \bigr)$ where
$\mathcal{L} := (\mathscr{O}_X,L_1, ...c, L_r)$ is a list of line bundles on a
projective toric variety $X$. The quiver $Q$ defines a smooth projective toric
variety, called the multilinear series $|\mathcal{L}|$, and a map $X \to
|\mathcal{L}|$. We provide necessary and sufficient conditions for the induced
map to be a closed embedding. As a consequence, we obtain a new geometric
quotient construction of projective toric varieties. Under slightly stronger
hypotheses on $\mathcal{L}$, the closed embedding identifies $X$ with the fine
moduli space of stable representations for the bound quiver $(Q,R)$.
