Charlie Barnett stars as Peter Mills, a young new academy graduate who follows a long line of multi-generational firefighters, in NBC's drama "Chicago Fire."   A graduate of The Juilliard School, he began performing in his hometown of Sarasota, Florida, at the age of seven in opera and musical theatre productions.   On the big screen, Barnett has a supporting role in "Men in Black 3" with Will Smith and Josh Brolin.  Other features include "Gayby," which premiered this year at the South by Southwest Film Festival, "The Happy Sad," a tangled love story, and "Private Romeo," a modern take on Romeo and Juliet.   On television, he has guest-starred on NBC's "Law and Order:SVU" and "Law and Order: CI."