Russell Crowe & Ryan Gosling -- Hail To The Chief ... Of LAPD

Two starstruck fans were on the set of the upcoming '70s thriller, "The Nice Guys" ... but this time the stars were the ones who were starstruck.

Russell Crowe and Ryan Gosling went goo goo over LAPD Chief Charlie Beck when he strolled onto the set for a quick look-see during filming outside downtown headquarters.

The trio shot the breeze and traded war stories, and they must have hit it off ... because we're told Beck invited them to stop by his office later.

As for the cast on Gosling's arm ... it's just for the flick.