  The rotation of asymmetric bodies in eccentric Keplerian orbits can be
chaotic when there is some overlap of spin-orbit resonances. Here we show that
the rotation of two coorbital bodies (two planets orbiting a star or two
satellites of a planet) can also be chaotic even for quasi-circular orbits
around the central body. When dissipation is present, the rotation period of a
body on a nearly circular orbit is believed to always end synchronous with the
orbital period. Here we demonstrate that for coorbital bodies in quasi-circular
orbits, stable non-synchronous rotation is possible for a wide range of mass
ratios and body shapes. We further show that the rotation becomes chaotic when
the natural rotational libration frequency, due to the axial asymmetry, is of
the same order of magnitude as the orbital libration frequency.
