We perform an analysis of the transverse coherence of the radiation from a TW level tapered hard X-ray Free Electron Laser (FEL). The radiation properties of the FEL are studied for a Gaussian, parabolic and uniform transverse electron
beam density profile in a 200 m undulator at a resonant wavelength of 1.5 Å. Simulations performed using the 3-D FEL particle code GENESIS show that diffraction of the radiation occurs due to a reduction in optical guiding in the
tapered section of the undulator. This results in an increasing transverse coherence for all three transverse electron beam profiles. We determine that for each case considered the radiation coherence area is much larger than the electron beam spot size, making coherent diffraction imaging experiments possible for TW X-ray FELs.