  We propose an application of a single Cooper pair box (Josephson qubit) for
active cooling of nanomechanical resonators. Latest experiments with Josephson
qubits demonstrated that long coherence time of the order of microsecond can be
achieved in special symmetry points. Here we show that this level of coherence
is sufficient to perform an analog of the well known in quantum optics
``laser'' cooling of a nanomechanical resonator capacitively coupled to the
qubit. By applying an AC driving to the qubit or the resonator, resonators with
frequency of order 100 MHz and quality factors higher than $10^3$ can be
efficiently cooled down to their ground state, while lower frequency resonators
can be cooled down to micro-Kelvin temperatures. We also consider an
alternative setup where DC-voltage-induced Josephson oscillations play the role
of the AC driving and show that cooling is possible in this case as well.
