We optically trap a single nanoparticle in high vacuum and cool its three spatial degrees of freedom by means of active parametric feedback. Using a single laser beam for both trapping and cooling we demonstrate a temperature compression ratio of four orders of magnitude. The absence of a clamping mechanism provides robust decoupling from the heat bath and eliminates the requirement of cryogenic precooling. The small size and mass of the nanoparticle yield high resonance frequencies and high quality factors along with low recoil heating, which are essential conditions for ground state cooling and for low decoherence. The trapping and cooling scheme presented here opens new routes for testing quantum mechanics with mesoscopic objects and for ultrasensitive metrology and sensing.