  The observation by the IceCube Collaboration of a high-energy ($E \gtrsim
200$ TeV) neutrino from the direction of the blazar TXS 0506+056 and the
coincident observations of enhanced $\gamma$-ray emissions from the same object
by MAGIC and other experiments can be used to set stringent constraints on
Lorentz violation in the propagation of neutrinos that is linear in the
neutrino energy: $\Delta v = - E/M_1$, where $\Delta v$ is the deviation from
the velocity of light, and $M_1$ is an unknown high energy scale to be
constrained by experiment. Allowing for a difference in neutrino and photon
propagation times of $\sim 10$ days, we find that $M_1 \gtrsim 3 \times
10^{16}$ GeV. This improves on previous limits on linear Lorentz violation in
neutrino propagation by many orders of magnitude, and the same is true for
quadratic Lorentz violation.
