  In the canonical model of Moon formation, a Mars-sized protoplanet "Theia"
collides with proto-Earth at close to their mutual escape velocity $v_{\rm
esc}$ and a common impact angle 45{\deg}. The "graze-and-merge" collision
strands a fraction of Theia's mantle into orbit, while Earth accretes most of
Theia and its momentum. Simulations show that this produces a hot, high angular
momentum, silicate-dominated protolunar system, in substantial agreement with
lunar geology, geochemistry, and dynamics. However, a Moon that derives mostly
from Theia's mantle, as angular momentum dictates, is challenged by the fact
that O, Ti, Cr, radiogenic W, and other elements are indistinguishable in Earth
and lunar rocks. Moreover, the model requires an improbably low initial
velocity. Here we develop a scenario for Moon formation that begins with a
somewhat faster collision, when proto-Theia impacts proto-Earth at ~1.2 $v_{\rm
esc}$, also around 45{\deg}. Instead of merging, the bodies come into violent
contact for a half-hour and their major components escape, a "hit-and-run
collision." N-body evolutions show that the "runner" often returns ~0.1-1 Myr
later for a second giant impact, closer to $v_{\rm esc}$; this produces a
postimpact disk of ~2-3 lunar masses in smoothed particle hydrodynamics
simulations, with angular momentum comparable to canonical scenarios. The disk
ends up substantially inclined, in most cases, because the terminal collision
is randomly oriented to the first. Proto-Earth contributions to the silicate
disk are enhanced by the compounded mixing and greater energy of a collision
chain.
