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This paper considers the problem of tracking airborne chemical plumes in 3-dimensions. Finding the source of a volatile chemical plume is considered to be a valuable capability for a mobile robot, with potential applications in areas such as locating chemical leaks, incipient fires, explosives, narcotics, plant material, and survivors of avalanches and earthquakes. Many of the robotic systems that are being developed for this task restrict themselves to a 2-dimensional search where the chemical sensor is held at a constant height above the ground. This may prevent the robot from tracking the plume close to its source, especially if the source is positioned high above the robot or close to the ground. In this project a search strategy for tracking chemical plumes in 3-dimensions has been developed and tested on a robot. This robot has a limited capability for sensing and following chemical plumes in 3-dimensions. This paper describes the search strategy and the robot that was developed to test it. Results of practical plume tracking experiments are also presented.