Karl Klotz submitted images from the CFD Special Operations warehouse which also houses vehicles assigned to the Equipment and Supply division.

Chicago FD Special Operations compressor unit 5-2-3. Karl Klotz photo

Chicago FD Equipment and Supply unit 6-4-14. Karl Klotz photo

Chicago FD Equipment and Supply unit 6-4-13. Karl Klotz photo
More images from the Special Operations warehouse are HERE and HERE.
#1 by Drew Smith on December 18, 2013 - 5:00 PM
You need this type of compressor to run an air knife which is commonly used with a ResQ Vac on trench collapses. It can also run jackhammers as Scott mentioned. You can also use it for low pressure air lifting bags. Unlike the breathing air compressors which are low-volume/high-pressure these twin-screw compressors are high-volume and achieve pressures of no more than a few hundred PSI compared to SCBA compressors which are usually 3000-6000 PSI.
#2 by Scott on December 18, 2013 - 4:51 PM
Odds are it is for pneumatic tools (jackhammers, etc) for structural collapse. Secondary, If it has the correct filters, then possibly a breathing air compressor for running any supplied air device for technical rescue.
#3 by CNix on December 18, 2013 - 4:12 PM
Curious as to what the compressor on 5-2-3 would be used for? And has it ever been used?