Whats the earliest you can catch raikou and entei?
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After you enter Ecruteak and walk down to the basement of the Burned Tower, all three legendaries, Entei, Raikou, and Suicune will begin to roam around the region. (The exception being Suicune as he shows up in specific locations).
It's certainly possible to catch Raikou immediately after that's done, but I would think it'd be pretty difficult, given what items you'd have available to you.