i don't think a vapor barrier is necessarily a good idea in chicago. why do you feel you need it? if the insulation (i assume fiberglass??) is loose, i would never try to hold it w/ 4 mil. i think, if something is needed, tyvek would be a better choice; it is far tougher and much more vapor permeable. if you don't HAVE to have some kind of sheet stuff, i'd suggest air sealing using the airtight drywall approach. that will require that all electrical boxes, light boxes, etc, be air tight as well. etc.
From Building Science;
"In addition to an air barrier at the ceiling line, a Class II vapor retarder (see sidebar) should be installed in Climate Zones 6 or higher (see Map 1).
Class I vapor retarders (i.e. vapor barriers – see sidebar) can be installed in vented attic assemblies in Climate Zones 6 or higher (see Map 1) but should be avoided in other climate zones as top side condensation can occur in summer months during air conditioning periods." From; http://www.buildingscience.com/documents/digests/bsd-102-understanding-attic-ventilation?full_view=1
I'd rather see Tyvek over the insulation, but not if you air-seal the attic first. Don't leave air pockets/cavities under the insulation after installing drywall ceiling from the wires, the insulation requires contact with drywall. Ask them if you can use unfaced batts after drywall, many departments do. They can check at final inspection.
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