Before or after the Pokemon League?
Beat the Pokemon League and enter the Hall of Fame.
Battle N in the ruins of N's Castle unground in Victory Road (Can only be accessed after entering the hall of Fame).
Beat N and get the Dark/ Light Stone (depending on the game) and take it to to the top of Dragonspiral Tower.
Battle and catch Zekrom/ Reshiram.
Go to the Giant Chasm and Kyurem will be there.
Unless you do all this, Kyurem will not appear at the Giant Chasm
After, since The Giant Chasm is only able to be accesed after the Pokemon League
After beating the game, you can return to the back of the Giant Chasm and catch a normal Kyurem. It is at level 70.
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