The Pixel Luminosity Telescope (PLT) is a dedicated luminosity monitor, presently under construction, for the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC). It measures the particle flux in three layers of pixel diamond detectors that are aligned precisely with respect to each other and the beam direction, utilizing simultaneously performed particle track position measurements. The PLT's single-crystal CVD diamonds are bump-bonded to the PSI46 pixel readout chip the same readout chip used in the silicon pixel system in CMS. Single-crystal CVD diamond pixel detectors have many attributes that make them desirable for use in charged particle tracking in radiation hostile environments such as the LHC. They are expected to withstand the radiation near the beam pipe over several years at full LHC luminosity with a modest loss of pulse height and no increase of leakage currents. In order to further characterize the applicability of diamond technology to charged particle tracking, the intrinsic spatial resolution of single-crystal CVD diamonds was measured using a high resolution beam telescope developed at the University of Zurich. We present the results of these studies.