The precise shape of the Sun has not been convincingly determined, despite half a century of modern photoelectric observations. The expected deviation of the solar-limb shape from a perfect circle is very small, but such asphericity is sensitive to the Sun's otherwise invisible interior conditions, as well as the solar atmosphere. We use evidence from a long-running experiment based in space to show that, when analyzed with sufficiently high spatial resolution, the Sun's oblate shape is distinctly constant and almost completely unaffected by the solar-cycle variability seen on its surface. The solar oblateness is significantly lower than theoretical expectations by an amount that could be explained by a slower differential rotation in the outer few percent of the Sun.