You do, but it's a very minor occurrence that doesn't really fit in with the story. You just happen to find Chernabog in his volcano, fight him, and continue onwards. He doesn't really feel like he belongs where he is. The party just finds him randomly, beats him and continue onward without even mentioning anything.
If I were you, I wouldn't worry too much, Kingdom Hearts as a whole is fairly tame, and, as a JRPG very simple.
The sequels make the plot a convoluted mess, it should be noted. This begins with Kingdom Hearts 2.
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