We describe a technique for the generation of an isolated burst of X-ray radiation with a duration of (approx) 100 attoseconds in a free electron laser (FEL) employing self-amplified spontaneous emission. Our scheme relies on an initial interaction of the electron beam with an ultra-short laser pulse in a one-period wiggler followed by compression in a dispersive section. The result of this interaction is to create a sub-femtosecond slice of the electron beam with enhanced growth rates for FEL amplification. After many gain lengths through the FEL undulator, the X-ray output from this slice dominates the radiation of the entire bunch. We consider the impact of various effects on the efficiency of this technique. Different configurations are considered in order to realize various timing structures for the resulting radiation.