  We study the equal-mass classical three rotor problem, a variant of the three
body problem of celestial mechanics. The quantum $N$-rotor problem has been
used to model chains of coupled Josephson junctions and also arises via a
partial continuum limit of the Wick-rotated XY model. In units of the coupling,
the energy serves as a control parameter. We find periodic 'pendulum' and
'breather' orbits at all energies and choreographies at relatively low
energies. They furnish analogs of the Euler-Lagrange and figure-8 solutions of
the planar three body problem. Integrability at very low energies gives way to
a rather marked transition to chaos at $E_c \approx 4$, followed by a gradual
return to regularity as $E \to \infty$. We find four signatures of this
transition: (a) the fraction of the area of Poincar\'e surfaces occupied by
chaotic sections rises sharply at $E_c$, (b) discrete symmetries are
spontaneously broken at $E_c$, (c) $E=4$ is an accumulation point of stable to
unstable transitions in pendulum solutions and (d) the Jacobi-Maupertuis
curvature goes from being positive to having both signs above $E=4$. Moreover,
Poincar\'e plots also reveal a regime of global chaos slightly above $E_c$.
