FM factory

I notice the builder plates say Chicago, IL - were the locomotives actually built in Chicago, or was it Beloit? (I understand the Erie-builts were built in Erie, PA)

Beloit. Photos exist of FM units-- including the first OP-engined switcher-- breaking through paper barriers at initial roll-out; if the captions are to be believed, this was at the Beloit FM plant.
Initially only small units could be built there. The contract with GE to build the Erie-builts was to give time for FM to build a suitable erecting hall at Beloit works. (Source: ??? but I've seen numerous histories of FM locomotive production, including Kirkland's "Locomotive Builders, vol. 1," and never gotten a contrary impression.)
Maybe Chicago was the site of some corporate offices?

The corporate offices of Fairbanks,Morse and Co. were indeed in Chicago.