The equator-to-pole radius difference (Δr=R eq−R pol) is a fundamental property of our star, and understanding it will enrich future solar and stellar dynamical models. The solar oblateness (Δ⊙) corresponds to the excess ratio of the equatorial solar radius (R eq) to the polar radius (R pol), which is of great interest for those working in relativity and different areas of solar physics. Δr is known to be a rather small quantity, where a positive value of about 8 milli-arcseconds (mas) is suggested by previous measurements and predictions. The Picard space mission aimed to measure Δr with a precision better than 0.5 mas. The Solar Diameter Imager and Surface Mapper (SODISM) onboard Picard was a Ritchey–Chrétien telescope that took images of the Sun at several wavelengths. The SODISM measurements of the solar shape were obtained during special roll maneuvers of the spacecraft by 30° steps. They have produced precise determinations of the solar oblateness at 782.2 nm. After correcting measurements for optical distortion and for instrument temperature trend, we found a solar equator-to-pole radius difference at 782.2 nm of 7.9±0.3 mas (5.7±0.2 km) at one σ. This measurement has been repeated several times during the first year of the space-borne observations, and we have not observed any correlation between oblateness and total solar irradiance variations.