  In this paper we study the smallest non-zero eigenvalue $\lambda_1$ of the
Laplacian on toric K\"ahler manifolds. We find an explicit upper bound for
$\lambda_1$ in terms of moment polytope data. We show that this bound can only
be attained for $\mathbb{CP}^n$ endowed with the Fubini-Study metric and
therefore $\mathbb{CP}^n$ endowed with the Fubini-Study metric is spectrally
determined among all toric K\"ahler metrics. We also study the equivariant
counterpart of $\lambda_1$ which we denote by $\lambda_1^T$. It is the the
smallest non-zero eigenvalue of the Laplacian restricted to torus-invariant
functions. We prove that $\lambda_1^T$ is not bounded among toric K\"ahler
metrics thus generalizing a result of Abreu-Freitas on $S^2$. In particular,
$\lambda_1^T$ and $\lambda_1$ do not coincide in general.
