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There actually seems to be several candidates to this title:
1) Vallée Blanche in Chamonix from Aiguille du Midi down to Chamonix. There are several different numbers given for this run between 20 and 22 km. The Chamonix home page claims 20 km. Note that this is not a piste, it's a commonly used off-piste route where a mountain guide should be used.
2) From Kleine Matterhorn to Zermatt. Ski-zermatt claims 13 km and zermatt home page claims 22 km.
3) The Sarenne run in Alpe d'Huez is often claimed as the longest piste. It's on the piste map (from the Alpe d'Huez home page) stated as 19 km but on the Alpe d'Huez home page itself it says 16 km so it's probably not the longest piste but it is the longest black piste, even though the last part of it is more transport than black.
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