Question

Before or after the Pokemon League?

Answer 1

1. Beat the Pokemon League and enter the Hall of Fame.

2. Battle N in the ruins of N's Castle unground in Victory Road (Can only be accessed after entering the hall of Fame).

3. Beat N and get the Dark/ Light Stone (depending on the game) and take it to to the top of Dragonspiral Tower.

4. Battle and catch Zekrom/ Reshiram.

5. Go to the Giant Chasm and Kyurem will be there.

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Unless you do all this, Kyurem will not appear at the Giant Chasm

Answer 2

After, since The Giant Chasm is only able to be accesed after the Pokemon League

Answer 3

After beating the game, you can return to the back of the Giant Chasm and catch a normal Kyurem. It is at level 70.