This looks like a model that was carefully set up to spin.
First the facts: FAR part 27 regulates the design criteria for rotorcraft. Specifically, FAR 27.337 states:
The rotorcraft must be designed for—
(a) A limit maneuvering load
factor ranging from a positive limit of 3.5 to a negative limit of
−1.0 [snip]
So yes, contrary to the unsubstantiated claims in the highest-rated answer, the inverted rotor shaft can support the weight of the (most likely empty) helicopter. The center of gravity is very close to the rotor mast, and gyroscopic forces might even stabilise the fuselage long enough to film one full revolution, but still the clip is impossible to film with a real helicopter without breaking things. Look at the drawing of the Hughes 500 C, the type used in the clip, below:

Hughes 500 three-side view (picture source)
Clearly, the tail extends above the rotor plane, so something must be broken first before the fuselage is free to spin around. Next, everything must be carefully set up and the fuselage must be spun around somehow. This film was not made after an inverted touchdown - this is impossible with regular helicopters. From the linked page:
To enable a commercial helicopter to fly upside down, manufacturers
would need to make its rotor blades more rigid so as not to flex too
close to the main body of the helicopter (otherwise they could rip off
their own fuselage or other critical components). They would also need
to redesign the joint that connects the rotor blades with the rest of
the vehicle so it could bear the load of an upturned helicopter.
Finally, they would need to develop new controls to allow the rotor
blades to tilt downwards and reconfigure the engine so that fuel and
lubricants could be distributed properly while the helicopter was
inverted.
The page doesn't go into stability, but that would be another reason why this clip is not real. Flying upside down would be similar to balancing a broom on a fingertip.
Note that the FAR part 27 still demands a load that is equal to standing the helicopter on its head, regardless of the blades touching the body when loaded for -1g. Even though the helicopter cannot be flown inverted, the loads that would incur must still be tolerated, because they might happen in regular flight when a heavy gust hits the aircraft.
My explanation: Someone took his model helicopter, broke part of the tail off (note that the vertical part of it is missing in the clip!) and carefully balanced it on its rotor head. Mind you, he could even have fixed the rotor head to the ground with some tent stakes. There is enough structure inside of the hinges to facilitate this. Spinning it is easy, and no, there are no imbalances which would "tear the helicopter apart", especially not at such a leisurely rotation speed.
EDIT: Thanks to the invaluable help of @PTwr it is now clear that this is a scene from the 1975 Disney movie "Escape to Witch Mountain" in which two kids are chased by an evil millionaire. His helicopter in one scene flies and lands upside down. From www.rotaryaction.com:
… The chopper winds up flying upside-down and landing in that
position, still spinning, making the pilot and his passenger dizzy.
So it is a Hollywood special effect, and given the time of the movie (before CGI), this must have been shot with a scale model.