Most VLF detectors including the E-Trac see a gold chain as a group of individual links. If you look at a single link you will see that it is around the size of a gold nugget smaller than 0.500 grams. Like an earring backing. The E-Trac is designed, tuned, and optimized to find high conductive coins and relics. It will find low conductive nickels and gold rings just fine because they are in the 5 gram range, not the 0.500 gram range. A chain's conductive size is broken and effectively the size of its links.
If you are looking for a gold chain you lost, the E-Trac would not be my choice of detector, to find it. You may be able to find it with an X-Terra 6" HF DD coil, a Tesoro Compadre, etc, if it is no deeper than an inch or two. I would go all metal, and dig shallow iron signals, as any signal, on a VLF detector, close to its limit of detection will fade to an iron signal and show up as a null if any discrimination is used. A small coil will help in detecting small gold, as long as it is not deep.
Air test the chain again in all metal!