Magnetoresistance is the change of a material's electrical resistance in response to an applied magnetic field. In addition to its intrinsic scientific interest, it is a technologically important property, placing it in "Pasteur's quadrant" of research value: materials with large magnetorsistance have found use as magnetic sensors 1, in magnetic memory 2, hard drives 3, transistors 4, and are the subject of frequent study in the field of spintronics 5, 6. Here we report the observation of an extremely large one-dimensional positive magnetoresistance (XMR) in the layered transition metal dichalcogenide (TMD) WTe2; 452,700 percent at 4.5 Kelvin in a magnetic field of 14.7 Tesla, and 2.5 million percent at 0.4 Kelvin in 45 Tesla, with no saturation. The XMR is highly anisotropic, maximized in the crystallographic direction where small pockets of holes and electrons are found in the electronic structure. The determination of the origin of this effect and the fabrication of nanostructures and devices based on the XMR of WTe2 will represent a significant new direction in the study and uses of magnetoresistivity.