There is SpecBas, which is a hybrid between an emulator and an enhanced version of Sinclair Spectrum BASIC.
https://sites.google.com/site/pauldunn/
It does require a host OS to run, though, so it does not entirely fit your bill.
Acorn's original RISC OS for the Archimedes is still alive, maintained, and runs on a variety of modern ARM hardware such as the Raspberry Pi and BeagleBoard range. It includes a lightning-fast BBC BASIC V interpreter as its primary programming language, although it is not written in BBC BASIC itself. (Although parts of it, and the ARM processor, were prototyped in BBC BASIC!)
https://www.riscosopen.org/content/
It only runs on ARM hardware, though. To run it on an x86 machine, you need an emulator, such as RPCEmu (FOSS) http://www.marutan.net/rpcemu/index.php or Virtual Acorn (commercial) http://www.virtualacorn.co.uk/
If you cast your net slightly wider, for instance to the Pascal family, then there is Native Oberon, which is a native PC operating system written entirely in the Oberon programming language. Not a trace of C or anything else. It's tiny, fast, efficient and designed to be easy to learn, understand and modify. http://ignorethecode.net/blog/2009/04/22/oberon/
** UPDATE **
I've found out about 2 new contenders that I did not know about when I posted my previous answer back in January.
The BASIC Engine fits your a bill: a very inexpensive, DIY 32-bit computer with a rich, powerful BASIC: https://basicengine.org/
And the MaxiMite: http://geoffg.net/Maximite_Story.html