  We report measurements on ultrathin (<10 nm) nanowires produced by coating
carbon nanotubes with a superconducting amorphous MoGe alloy. We find that
nanowires can be superconducting or insulating depending on their normal state
resistance $R_{N}$ compared to $R_{q}=h/(2e)^{2}$ -- the quantum resistance for
Cooper pairs. If $R_{N}< R_{q}$ the tunneling of quantum phase slips (QPS) is
prohibited due to strong damping, and so the wires stay superconducting. The
insulating state, observed if $R_{N}> R_{q}$, is explained in terms of
proliferation of quantum phase slips and corresponding localization of Cooper
pairs. The observed superconductor-insulator transition is analogous to the
dissipative phase transition which takes place in Josephson Junctions at
$R_{N}= R_{q}$ (Penttila et al., Phys. Rev. Lett. Vol.82, p.1004, 1999)
