  Using a variational method, we exhibit a surprisingly simple periodic orbit
for the newtonian problem of three equal masses in the plane. The orbit has
zero angular momentum and a very rich symmetry pattern. Its most surprising
feature is that the three bodies chase each other around a fixed eight-shaped
curve. Setting aside collinear motions, the only other known motion along a
fixed curve in the inertial plane is the ``Lagrange relative equilibrium" in
which the three bodies form a rigid equilateral triangle which rotates at
constant angular velocity within its circumscribing circle. Our orbit visits in
turns every ``Euler configuration" in which one of the bodies sits at the
midpoint of the segment defined by the other two (Figure 1). Numerical
computations by Carles Sim\'o, to be published elsewhere, indicate that the
orbit is ``stable" (i.e. completely elliptic with torsion). Moreover, they show
that the moment of inertia I(t) with respect to the center of mass and the
potential U(t) as functions of time are almost constant.
