  For the three body problem with equal masses, we prove that the most
symmetric continuation class of Lagrange's equilateral triangle solution, also
referred to as the $P_{12}$ family of Marchal, contains the remarkable figure
eight choreography discovered by Moore in 1993, and proven to exist by
Chenciner and Montgomery in 2000. This settles a conjecture of Marchal which
dates back to the 1999 conference on Celestial Mechanics in Evanston Illinois,
celebrating Donald Saari's 60th birthday.
