  The gravitational wave signal GW150914, recently detected by LIGO and Virgo
collaborations, is used to place a bound on the scale of quantum fuzziness of
non-commutative space-time. We show that the leading non-commutative correction
to the phase of the gravitational waves produced by a binary system appears at
the 2nd order of the post- Newtonian expansion. This correction is proportional
to $\Lambda^2 \equiv |\theta^{0i}|^2/(l_P t_P)^2$, where $\theta^{\mu \nu}$ is
the antisymmetric tensor of non-commutativity. To comply with GW150914 data, we
find that $\sqrt{\Lambda} \lesssim 6$, namely less than one order of magnitude
above the Planck scale. This is the most stringent bound on non-commutative
scale, exceeding the previous constraints from particle physics processes by
$\sim 15$ orders of magnitude.
