We explore the possibility of using a relativistic plasma density wave as a wiggler for producing free-electron laser radiation. Such a wiggler is a purely electric wiggler with frequency ω
p(plasma frequency) and wavenumber k
p. If an electron beam is injected parallel to the plasma wave wavefront, it is wiggled transversely with an apparent wiggler wavelength

. Using plasma densities in the 10
17(cm
-3) range, λ
wof order 100 μm may be obtained, thereby permitting generation of short wavelength radiation with modest energy beams. The effective wiggler strength

can be extremely large. We discuss the excitation methods for such wigglers and examine the constraints imposed by the plasma medium on FEL gain in this scheme.