Conventional multiple track location shear wave elasticity imaging (MTL-SWEI) is a powerful tool for noninvasively estimating tissue elasticity. The resolution and noise of MTL-SWEI systems, however, are limited by ultrasound speckle. Single track location SWEI (STL-SWEI) is a novel variant which fixes the position of the tracking beam and modulates the push location to effectively cancel out the effects of speckle bias. We present a 3D STL-SWEI system which provides full suppression of lateral and elevation speckle bias for high resolution 3D elasticity imaging, and requires no inherent spatial filtering to make precise measurements of shear wave speed. The system is demonstrated in a uniform elasticity phantom.