His chest rig is actually two different rigs combined.
You can find a similar configuration on Military Morons, but try as i might i can not find the pic to link to. sorry 'bout that.
Rear panel rig. Either a reverse worn micro-chest rig or a "tailgunner" rig:
check out mm's second line gear page 2, its the second review from bottom.
And the Chest rig could be either a blackhawk RRV or a Paraclete RACK, with the bib folded down.
The intent is that if Price has to ditch the main rig, hes still got that small rig, and you'll notice (in both MW2 and MW3), he's got his survival kit pouch and an extra pistol mag pouch on there.
Soap and most other characters in MW3 do the same thing with the survival pouch/medic pouch. look next time you play.
I could be over analysing, but its the concept of first line and second line gear.
Cheers