The International Linear Collider (ILC) and other proposed high energy e+e- machines aim to measure with unprecedented precision Standard Model quantities and new, not yet discovered phenomena. One of the main requirements for achieving this goal is a measurement of the incident beam energy with an uncertainty close to 10-4. This article presents the analysis of data from a prototype energy spectrometer commissioned in 2006-2007 in SLAC's End Station A beamline. The prototype was a 4-magnet chicane equipped with beam position monitors measuring small changes of the beam orbit through the chicane at different beam energies. A single bunch energy resolution close to 5.10-4 was measured, which is satisfactory for most scenarios. We also report on the operational experience with the chicane-based spectrometer and suggest ways of improving its performance.