It is. You usually need a bootstrap version of the language either compiled or interpreted from another language.
And to bend your mind a little more, years ago I read the history of a Pascal compiler written as a grad student project. It written in Pascal and compiled with the system's built-in Pascal compiler. Eventually, it was good enough to replace the system's built-in Pascal compiler. Unfortunately, they found a bug in code generation, but the fix for the code generator triggered the bug in the compiler, generating a bad compiler. To fix it required hand-patching the binaries from the installed compiler to then apply the patch to the source to replace itself.