A full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations. The major features of the approach are : 1) an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined, and 2) the design is accomplished by using a partial-fraction expansion separating the unstable part from the system and then applying well-known finite dimensional state vector techniques. A procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer.