Claude Lelouch's 1976 short film Rendezvous (YouTube video) is legendary:

On an August morning in 1978, French filmmaker Claude Lelouch mounted a gyro-stabilized camera to the bumper of a Ferrari 275 GTB and had a friend, a professional Formula 1 racer, drive at breakneck speed through the heart of Paris.

No streets were closed, for Lelouch was unable to obtain a permit.
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Filmed in 1976, the revered short film by seminal French director Claude Lelouch is regarded as the ultimate in chase scenes - the connoisseurs' trump card in response to Bullitt or The French Connection.

If you thought that was cool, check out the Google Maps + Google Video Mashup of Claude Lelouch's Rendezvous that allows you to track the progress on a Google Map. Awesome...