One-third of Sun-like stars are born with misaligned planet-forming disks.

Exoplanets are organized in a broad array of orbital configurations that reflect their formation along with billions of years of dynamical processing through gravitational interactions. This history is encoded in the angular momentum architecture of planetary systems-the relation between the rotational properties of the central star and the orbital geometry of planets. A primary observable is the alignment (or misalignment) between the rotational axis of the star and the orbital plane of its planets, known as stellar obliquity. Hundreds of spin-orbit constraints have been measured for giant planets close to their host stars, many of which have revealed planets on misaligned orbits. A leading question that has emerged is whether stellar obliquity originates primarily from gravitational interactions with other planets or distant stars in the same system, or if it is 'primordial'-imprinted during the star-formation process. Here we present a comprehensive assessment of primordial obliquities between the spin axes of young, isolated Sun-like stars and the orientation of the outer regions of their protoplanetary disks. Most systems are consistent with angular momentum alignment but about one-third of isolated young systems exhibit primordial misalignment. This suggests that some obliquities identified in planetary systems at older ages-including the Sun's modest misalignment with planets in the Solar System-could originate from initial conditions of their formation.