Dimension of the stalk at the point in the closure of an open subscheme

Question

Let $U$ be an open subscheme of $X$ a $\mathbb C$-scheme locally of finite type. I know that $U$ is of dimension $n$ and I have a point $x$ in the closure of $U$. What can be said of the Krull dimension of $\mathcal O_{X,x}$? A reference or explanation would be much appreciated!