  The infall of the Large Magellanic Cloud (LMC) is predicted to displace the
inner Milky Way (MW), imprinting an apparent 'reflex motion' on the observed
velocities of distant halo stars. We construct the largest all-sky
spectroscopic dataset of luminous red giant stars from $50-160$ kpc, including
a new survey of the southern celestial hemisphere. We fit the full 6D
kinematics of our data to measure the amplitude and direction of the inner MW's
motion towards the outer halo. The observed velocity grows with distance such
that, relative to halo stars at $100$ kpc, the inner MW is lurching at $\approx
40$ km s$^{-1}$ towards a recent location along the LMC's past orbit. Our
measurements align with N-body simulations of the halo's response to a $1.8
\times 10^{11} M_\odot$ LMC on first infall, suggesting that the LMC is at
least 15% as massive as the MW. Our findings highlight the dramatic
disequilibrium of the MW outskirts, and will enable more accurate measurements
of the total mass of our Galaxy.
