The James Webb Space Telescope (JWST) will be a 6-meter diameter segmented reflector that will be launched at room temperature and passively cooled to about 40 Kelvin at the L2 point. Because of the large thermal load, understanding the thermophysical properties of the mirror, secondary optics, and supporting structure materials is crucial to the design of an instrument that will provide diffraction limited performance at 2 microns. Once deployed, JWST will perform continuous science without wave front re-calibrations for durations ranging from one day to a month. Hence understanding of how small temperature fluctuations will impact the nanometric stability of the optical system through thermal expansion is required. As a result, the JWST materials testing team has designed and built a novel cryogenic dilatometer capable of coefficient of thermal expansion (CTE) measurements of ULE accurate to ~ 1.6 and 0.1 ppb/K for a nominal CTE = 30 ppb/K and 20 and 280 K thermal loads, respectively. The dilatometer will be used to measure the CTE of samples from JWST primary mirror prototypes, local CTE variations from multiple locations on a prototype mirror, CTE variations from batch to batch of the same material, and thermal and mechanical creep measurements from room temperature down to 30 K.