Would there be legal issues involved in putting a parody of a song in a book?

At one point of one of my stories, one of the characters sings/performs to a (self-created) parody of an existing song. Would the copyright issues that would be present if using the exact lyrics of the song still exist if using mostly original lines (the chorus is almost identical and it is painfully obvious what the original song is), or would that be averted due to having different lyrics than the original?