Gold & Silver Roaming Johto
Once the Burned Tower wakes them, Raikou, Entei, and Suicune wander Johto's grass at random. Each bolts the instant you cross its path. Running all three to ground is the region's great chase.
Roaming Johto is in Johto. In the story it comes after Route 39 and before Olivine City.
ROAMING JOHTO MAP
Pokemon Encounters
Raikou, Entei, and Suicune all roam Johto in Gold and Silver, three legendary beasts that never hold still. Each one flees the instant the battle starts, so bring a Pokemon that can trap them and a bag full of Ultra Balls.
Entei
Roaming Johto Guide
Patience, plus a way to stop them fleeing. After scattering from the Burned Tower, Raikou, Entei, and Suicune drift across Johto's routes at level 40, and all three run on the first turn you meet them. A move like Mean Look pins them down so you can wear them out, or just save the Master Ball for one.