The present invention is generally directed to substantially pure cannabidiol, stable cannabinoid pharmaceutical formulations, and methods of their use. In one aspect, the present invention is directed to a stable pharmaceutical formulation for oral administration comprising 10-32% (w/w) cannabidiol, 50-90% (w/w) caprylic/capric triglyceride, and 0.1-1.0% (w/w) alpha tocopherol.