alt Hacker NewsI don't think it's yet complete enough to compile itself; though I haven't looked at the assembler code, I'm pretty sure it requires bitwise operations the compiler can't compile yet. Also, the compiler itself requires things like null, symbolp, eq, and atom, which it also doesn't implement yet. Without those I'm not sure that it's fair to describe its input language as Lisp, though it does support car and cdr.
But it's still super cool. A really great thing about Lisp for purposes like this is that you don't get hung up on syntax and parsing, which is the most salient part of writing a compiler but not the most important.
Things like atom and symbols are functions in the runtime. A Lisp compiler only has to handle special forms, and function calls. If we see the compiler source code using a special operator that it doesn't handle, either directly using it or via macro expansion, then we know it's not yet self-hosting.