The rotational histories of irregularly shaped satellites are studied and are found to differ from the standard picture of tidal evolution of satellite rotations. Prior to capture into the synchronous rotation resonance, a narrow attitude-unstable chaotic zone is entered and the satellite begins to tumble chaotically. It is noted that enhanced dissipation of energy during the chaotic-tumbling phase may effect the orbital evolution. The theory suggests that, eventually, the rotation stays close to one of the accessible attitude-stable islands long enough for the weak tidal torque to remove the satellite from the chaotic zone.