Let $u\in H^1_{\mathrm{loc}}(U)$ be a weak solution of \begin{align*} -\sum_{i,j=1}^n \partial_{x_i}\big(a_{ij}(x)\partial_{x_j}u\big)=0 \end{align*} in $U$, where the coefficients $a_{ij}:U\to\mathbb R$ are measurable and there exist constants $0<\theta\le \Theta<\infty$ such that \begin{align*} \sum_{i,j=1}^n a_{ij}(x)\xi_i\xi_j\ge \theta |\xi|^2, \qquad |a(x)\xi|\le \Theta|\xi| \end{align*} for a.e. $x\in U$ and every $\xi\in\mathbb R^n$. Then $u$ has a locally Hölder continuous representative: whenever $V\subset\subset W\subset\subset U$, there are $\alpha\in(0,1)$ and $C>0$, depending on $n$, $\theta$, $\|a\|_{L^\infty(W)}$, $V$, and $W$, such that \begin{align*} \|u\|_{C^{0,\alpha}(V)}\le C\|u\|_{L^2(W)}. \end{align*}