Radiative heat transfer can be significantly enhanced via photon tunneling through a nanometer-scale gap to the point that it exceeds the blackbody limit. Here we report quantitative measurements of the near-field thermal radiation between doped-Si plates (width = 480 mu m and length = 1.34 cm). A novel MEMS-based platform enables us to maintain doped-Si plates at nanoscale gap distances that cannot be achieved by other methods. The measured radiative heat transfer coefficient was found to be 2.91 times greater than the blackbody limit at a 400-nm vacuum gap.