We aim to observe a chemical reaction in real time using gas-phase X-ray diffraction. In our initial experiment at the Linac Coherent Light Source (LCLS), we investigated the model system 1,3-cyclohexadiene (CHD) at very low vapor pressures. This reaction serves as a benchmark for numerous transformations in organic synthesis and natural product biology. Excitation of CHD by an ultraviolet optical pulse initiates an electrocyclic reaction that transforms the closed ring system into the open-chain structure of 1,3,5-hexatriene. We describe technical points of the experimental method and present first results. We also outline an approach to analyze the data involving nonlinear least-square optimization routines that match the experimental observations with predicted diffraction patterns calculated from trajectories for nonadiabatic vibronic wave packets.