We present new measurements of the coherent motion of galaxies based on observations of the large-scale redshift--space distortions seen in the two--dimensional two--point correlation function of Luminous Red Galaxies in Data Release Seven of the Sloan Digital Sky Survey. We have developed a new methodology for estimating these coherent motions, which is less dependent on the details of galaxy bias and of the cosmological model to explain the late--time acceleration of the expansion of the Universe. We measure a one--dimensional velocity dispersion of galaxies on large--scales of sigma_v=3.01^{+0.45}_{-0.46} Mpc/h and sigma_v=3.69^{+0.47}_{-0.47} Mpc/h at a mean redshift of z=0.25 and 0.38 respectively. These values are fully consistent with predictions for a WMAP7--normalised LCDM Universe and inconsistent (at >5 sigma) with a Dvali-Gabadadze-Porrati (DGP) model for the Universe. We can convert the units of these sigma_v measurements to 270^{+40}_{-41} km/s and 320^{+41}_{-41} km/s respectively (assuming a LCDM universe), which are much lower than that expected based on recent low redshift (z<0.2) measurements of the peculiar velocity field (or ``bulk flows"), i.e., we would have predicted motions of ~ 600 km/s over our redshift range (0.16 < z <0.47) to be consistent with these local measurements. One possible explanation for such a large discrepancy is that our Galaxy is located in unusually over, or under, dense region of the Universe.