The shape of the Sun subtly reflects its rotation and internal flows. The surface rotation rate, approximately 2 kilometers per second at the equator, predicts an oblateness (equator-pole radius difference) of 7.8 milli-arc seconds, or approximately 0.001%. Observations from the Reuven Ramaty High-Energy Solar Spectroscopic Imager satellite show unexpectedly large flattening, relative to the expectation from surface rotation. This excess is dominated by the quadrupole term and gives a total oblateness of 10.77 +/- 0.44 milli-arc seconds. The position of the limb correlates with a sensitive extreme ultraviolet proxy, the 284 angstrom limb brightness. We relate the larger radius values to magnetic elements in the enhanced network and use the correlation to correct for it as a systematic error term in the oblateness measurement. The corrected oblateness of the nonmagnetic Sun is 8.01 +/- 0.14 milli-arc seconds, which is near the value expected from rotation.