The maximum leaf spanning tree (MLST) is a good candidate for constructing a virtual backbone in self-organized multihop wireless networks, but is practically intractable (NP-complete). Self-stabilization is a general technique that permits to recover from catastrophic transient failures in self-organized networks without human intervention. We propose a fully distributed self-stabilizing approximation algorithm for the MLST problem in arbitrary topology networks. Our algorithm is the first self-stabilizing protocol that is specifically designed to approximate an MLST. It builds a solution whose number of leaves is at least 1/3 of the maximum possible in arbitrary graphs. The time complexity of our algorithm is O(n^2) rounds.