FYI, Public and private application deadline dates:

Parker: Sibling app 11/15, Non-sibling app 12/1
U of C Lab: 11/30
Latin: 12/1
Chicago Academy for the Arts: 12/3; auditions on 12/8
CPS - Chi Arts: 12/14
CPS - Von Steuben: 12/14
CPS - All Selective Enrollment Schools: 12/14
CPS - All IB (International Baccalaureate) programs (LPHS, Ogden, Senn, etc.): 12/14
CPS - Lincoln Park Double Honors: 12/14
CPS - Lincoln Park Performing Arts: 12/14
CPS - Senn Performing Arts: 12/14
British School and Lycee Francais: Rolling admissions. No particular deadline.
Catholic schools: Schedule a shadow day ASAP. There is nothing else to do until your child sits for exam on Saturday, 1/12. Application material is handed out that morning.
Waldorf: 1/15
Illinois Math and Science Academy (IMSA): 3/1