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For two metric spaces $\mathbb X$ and $\mathcal Y$, the chromatic number$\chi(\mathbb X;\mathcal Y)$ of $\mathbb X$ with forbidden $\mathcal Y$ is thesmallest $k$ such that there is a coloring of the points of $\mathbb X$ with$k$ colors and no monochromatic copy of $\mathcal Y$. In this paper, we showthat for each finite metric space $\mathcal{M}$ that contains at least twopoints the value $\chi\left(\mathbb R^n_\infty; \mathcal M \right)$ growsexponentially with $n$. We also provide explicit lower and upper bounds forsome special $\mathcal M$.

All finite sets are Ramsey in the maximum norm