Let $U\subset\mathbb{R}^n$ be open, and let $A\in L^\infty(U;\mathbb{R}^{n\times n})$ be a real symmetric matrix field uniformly elliptic with constants $\theta$ and $\Theta$. Let $u\in H^1_{\mathrm{loc}}(U)$ be a weak solution of \begin{align*} -\sum_{i,j=1}^n \partial_{x_i}\left(A_{ij}\partial_{x_j}u\right)=0 \end{align*} in $U$. If $V\Subset W\Subset U$ are open sets, then there exist $\gamma\in(0,1)$ and $C>0$, depending on $n$, $\theta$, $\Theta$, and the compact-containment geometry of $V\Subset W$, such that $u$ has a representative in $C^{0,\gamma}(V)$ and \begin{align*} \|u\|_{L^\infty(V)} + \sup_{\substack{x,y\in V\\x\ne y}}\frac{|u(x)-u(y)|}{|x-y|^\gamma} \le C\|u\|_{L^2(W)}. \end{align*}