We introduce a challenging problem in establishing and initially configuring a Free Space Optical (FSO) network. In such networks, it is assumed that each communication node is a base station, including a router and optical transceivers, and its number of transceivers is limited. In addition, the FSO networks are characterized by narrow beam, directional links (operating at 1550 nm, for example). The problem is to initially configure the transceivers to form a connected topology-an NP-complete problem because of the transceiver limitation. It also needs to configure the transceivers in a "distributed" fashion, because a node can have direct knowledge of only its neighbors. We have developed a fully distributed approximation algorithm, which constructs a spanning tree with maximal node degree at most one larger than that in the optimal solution. Due to its distributed nature, this algorithm outperforms known serial algorithms. For a graph with 200 nodes generated in some randomized model, speedups greater than 6 have been demonstrated.