By means of laser tweezers we have trapped a pair of microspheres that had been tethered by a double stranded, 10 kB DNA chain of 3.38 um in length. Using high speed imaging (1350 frames per second) and a novel three dimensional tracking method we have measured the thermal fluctuations in the position of these tethered spheres, and in untethered reference beads, for a series of surface to surface separations ranging from 1.2 um to 3.0 um. For smaller separations the transverse and longitudinal position cross-correlations for the tethered and untethered beads are very similar; for larger separations they show significant differences. We relate these new results to those of previous workers and compare with the results of Brownian Dynamic simulations.