  We show that the vibrations of a nanomechanical resonator can be cooled to
near its quantum ground state by tunnelling injection of electrons from an STM
tip. The interplay between two mechanisms for coupling the electronic and
mechanical degrees of freedom results in a bias-voltage dependent difference
between the probability amplitudes for vibron emission and absorption during
tunneling. For a bias voltage just below the Coulomb blockade threshold we find
that absorption dominates, which leads to cooling corresponding to an average
vibron population of the fundamental bending mode of 0.2.
