Fairly sure the US Army is #1 by most measures.
As well as BRS (500+) and CHC (240), the top civil operators in terms of fleet size would include AMC (400), Avincis (350 via Inaer/Bond) and PHI (250), with AMGH (220 via AEL/MTC/Reach/EagleMed) and Era (170) close behind. Non-military goverment fleets like the US DOS (215) and US CBP (150) could also have a claim for inclusion.
I/C