Golden Fleece
Chain of office of a Knight of the Order of the Golden Fleece.
The Golden Fleece was founded in the Kingdom of Burgundy in 1430, and included only a few dozen knights at any given time; it was considered the most prestigious order to be a part of. It’s still around, by the way, having weathered political upheavals and the end of the Habsburg monarchy. According to Wikipedia it counts amongst its members a number of Belgian / German / Austrian / Bohemian dukes and princes.
I think I remember reading that the little coats of arms on this chain reflected the current membership, so I figure they had to be changed every now and then as members joined or retired.
Also if I’m reading Wikipedia correctly, a lot of the treasures on display in this museum technically belong to the Golden Fleece and not the Austrian state, including the Imperial Cross with its reliquaries.