Laser cooling has given a boost to atomic physics throughout the last 30 years, as it allows one to prepare atoms in motional states, which can only be described by quantum mechanics. Most methods rely, however, on a near-resonant and cyclic coupling between laser light and well-defined internal states, which has remained a challenge for mesoscopic particles. An external cavity may compensate for the lack of internal cycling transitions in dielectric objects and it may provide assistance in the cooling of their centre-of-mass state. Here we demonstrate cavity cooling of the transverse kinetic energy of silicon nanoparticles freely propagating in high vacuum (<10(-8) mbar). We create and launch them with longitudinal velocities down to v≤1 m s(-1) using laser-induced ablation of a pristine silicon wafer. Their interaction with the light of a high-finesse infrared cavity reduces their transverse kinetic energy by up to a factor of 30.