During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as a foundation for more sophisticated algorithms. In this paper, we consider the problem of obtaining a vertex coloring as such an initial structure. We propose an algorithm that works under the unstructured radio network model. This model captures the characteristics of newly deployed ad hoc and sensor networks, i.e. asynchronous wake-up, no collision-detection, and scarce knowledge about the network topology. Our algorithm produces a correct coloring with O(Δ) colors in time O(Δ log n) with high probability in a unit disk graph, where n and Δ are the number of nodes in the network and the maximum degree, respectively. Furthermore, the number of locally used colors depends only on the local node density.