Thanks Yawgmoth and adrianxw.
I was giving myself a headache trying to comprehend how to do this. My first thought was that it was impossible and I started writing a sarcastic response... Then, I got a little more humble... I know a lot about electronics and computers, but I'm not a CS expert!
After all that thinking... I think it is possible to write a language exclusively in that language if that language includes it's own assembly language! In that case, you'd still, in effect, be starting with the CPU's machine language. I dunno if that has ever been done, but it would be interesting. You would have all the low level assembly stuff directly available to you without invoking a separate assembler.