Neighbor discovery is an essential part of the communication link establishment process for any wireless ad-hoc network. This problem of discovering neighbor nodes becomes even more challenging when the transceivers are highly directional. In this paper, we consider a 3D network of unmanned-aerial-vehicles (UAVs) that uses free-space-optical (FSO) transceivers for establishing high speed highly directional communication links. We consider that each UAV is equipped with a spherical structure on which multiple FSO transceivers are placed. The UAVs can electronically steer their communication beams by switching from one transceiver to another. We provide analysis on how optimally placing the transceivers with the appropriate divergence angles can help establish an FSO link at any direction in the 3D space. We also present a neighbor discovery algorithm that ensures discovery within a limited time. We demonstrate through extensive simulations that a UAV with FSO transceivers can successfully discover its neighbor UAVs even without prior location information about them and without any additional omnidirectional radio frequency (RF) channel.