Update: Resolution will take place early next week. You will not need to complete the chapter again.

Chadd "Celestalon" Nervigg came out to play on reddit to keep everyone in the loop on the legendary quest bug that some players have encountered.

For those not in the know, the Legendary Quest was not properly handed out to all players when logging in, so when they completed the adventure and then logged back into Hearthstone, it is no longer possible to earn credit for the quest. Thankfully, this is only a minor frustration and doesn't break anything else, so once a resolution is pushed out, you'll be able to open those sweet packs.

We don't know when the issue will be resolved at this time, but we should see another update from Blizzard once the fix goes out.

Quote From HS_Celestalon

We're working on a fix for this, sorry about that. Stay tuned!

Update - 2:45 PM Eastern June 18

Quote From Blizz_Kauza

Thank you to everyone who reported issues with completing the Legendary Quest for the new adventure. For players who completed the adventure shortly after it was released, it’s possible that you didn’t yet have the Legendary Quest and won’t be able to complete it with repeated playthroughs. We’re working on a fix that will check for adventure completion and whether you’ve gotten your rewards and grant quest completion to anyone who didn’t receive it. You will not need to complete the adventure again as long as you have completed it once. We’re likely going to get this fix out early next week.