I know that Crucible can drop the Gjallarhorn but I don't really know if Vanguard ROC can drop it too. Can someone tell me please? I'm very curious.
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Raid bosses are probably your best chance, I've gotten one from Atheon and Crota.
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Yes it can but I would suggest doing the templar on hard and get the gorgon cave chest on all 3 characters and to kill Atheon on all characters my one friend got gjallahorn from Crota on hard Wednesday.
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You can get any exotic anywhere. Besides bounty ones and raid ones.