  Levitated nano-oscillators are seen as promising platforms for testing
fundamental physics and testing quantum mechanics in a new high mass regime.
Levitation allows extreme isolation from the environment, reducing the
decoherence processes that are crucial for these sensitive experiments. A
fundamental property of any oscillator is its line width and mechanical quality
factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as
high as $10^{12}$ have been predicted for levitated systems, but to date, the
poor stability of these oscillators over long periods have prevented direct
measurement in high vacuum. Here we report on the measurement of an
ultra-narrow line width levitated nano-oscillator, whose line width of
$81\pm\,23\,\mu$Hz is only limited by residual gas pressure at high vacuum.
This narrow line width allows us to put new experimental bounds on dissipative
models of wavefunction collapse including continuous spontaneous localisation
and Di\'{o}si-Penrose and illustrates its utility for future precision
experiments that aim to test the macroscopic limits of quantum mechanics.
