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Someone who is an heir to the throne, or next in line to fill a usually important position, whether that be within a large company or government. It can be used metaphorically as well; often times rappers will claim to be a babychief, which basically means they're saying they will be the next big thing in the rap game.
Did you hear about Terrell? I heard him spitting fuego about how he thinks he's rap's babychief.
by Guap Daddy April 09, 2012