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 ω2 that is either incommensurate to the drive, or frequency-locked to it, ω2 = (p/q)•ω. 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 ω2/ω exhibits a Devil's staircase. A transition to chaotic motion is observed as resonances overlap.