<p>Controlling the motion of nanoscale objects at the quantum limit promises opportunities to test fundamental quantum physics and advances in quantum sensing. Rotational motion is of particular interest, as its nonlinear dynamics in a compact, closed configuration space provides access to phenomena such as rotational interferometry, tunnelling between angular configurations and quantum-enhanced torque sensing. A key requirement for such experiments is the capability to trap nanorotors and cool their orientation close to the two-dimensional librational quantum ground state. When rotational motion is confined in a harmonic potential, it becomes librational. Here we demonstrate that coherent scattering into a high-finesse cavity enables the ground-state cooling of two orthogonal librational modes of an optically levitated SiO₂ nanoparticle. Using a laser-induced desorption loading technique, we trap and cool several dimers and trimers of silica nanospheres to their respective ground states, all within a single day. The simultaneous cooling of both librational degrees of freedom allows us to align an individual nanorotor with respect to a space-fixed axis with an angular precision better than 20 µrad—close to the quantum-mechanical zero-point fluctuations.</p>