Spitfire.

This is coolbert:

A propeller-driven plane supersonic? A propeller-driven plane? Supersonic?

Close but not quite!

Thanks to the BBC and the article by Stephen Dowling. 

"The Spitfires that nearly broke the sound barrier"

"A handful of British Spitfire pilots cheated death in high-speed dives that helped pave the way towards supersonic flight."

The single greatest impediment to a propeller-driven aircraft achieving supersonic speed the propeller itself. A propeller creating  too much "drag, buffeting and noise".

Even with the advent of the jet engine research continuing into the development of a high-speed propeller-driven aircraft. A warplane not able to exceed the sound barrier but close. 

Warning! The following You Tube video contains a slight amount of material of an adult and risque' nature some may find offensive. View at your own discretion. You have been warned! Additionally turn down the volume level on your speakers prior to viewing the video.

See also from another Internet web site further research into the propeller-drive supersonic warplane. XF-88 Voodoo. Once more a concept that was "fly-able" but never placed into production or service.

coolbert.