Smooth Riemannian metric is locally real analytic?

Question

Let $U$ be an open subset of $\mathbb{R}^n$ and $g$ be a $C^\infty$ Riemannian metric on $U$. Given a point $x_0\in U$, does there exist a local neighborhood $x_0\in V\subset U$ and new coordinates thereon so that the components of $g$ with respect to the new coordinates are real analytic (i.e. is it possible to change coordinates so that the metric components are real analytic in the new coordinates, at least locally)?