Programming languages aren’t programs, hence they’re not “written” in any language. They are often described by formal grammars (e.g. BNF).
Interpreters and compilers for programming languages are programs and so must be written in some kind of programming language.
Go has at least two compilers, gc and gccgo. The former was written in C, but is now written in Go itself. While the latter is a gcc frontend written mainly in C++. Go’s libraries are written in Go.