  We study a plasma instability in semiconductor superlattices irradiated by a
monochromatic, pure AC electric field. The instability leads to sustained
oscillations at a frequency \omega 2 that is either incommensurate to the
drive, or frequency-locked to it, \omega 2 = (p/q) \omega. A spontaneously
generated DC bias is found when either p or q in the locking ratio are even
integers. Frequency locked regions form Arnol'd tongues in parameter space and
the ratio \omega 2 / \omega\ exhibits a Devil's staircase. A transition to
chaotic motion is observed as resonances overlap.
